Lots-of-LoRAs/task1424_mathqa_probability huggingface dataset:
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability t that all 3 jellybeans removed from the bag are blue ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: there is a 75 % chance that tigers will not win at all during the whole season . there is a 25 % chance that germany will not play at all in the whole season . what is the greatest possible probability that the tigers will win and germany will play during the season ? 
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 80 %
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a question paper has 2 parts , a & b , each containing 6 questions . if a student has to choose 4 from part a & 3 from part b , in how many ways can he choose the questions ? 
Options: a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: if 4 people are selected from a group of 9 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 85 , c ) 1 / 3 , d ) 56 / 85 , e ) 11 / 85
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 150 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? 
Options: a ) 110 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Output: 


Output: a
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: 5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope . the letter is said to be put in correct position if for example letter 1 goes into envelope 1 . now what is the probability that all letters be put into wrong envelopes ? 
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 11 / 120 , d ) 11 / 30 , e ) 76 / 120
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: three unbiased coins are tossed , what is the probability of ge ƫ ng at least 2 tails ? 
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 8 , e ) none of these
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: the probability that a number selected at random from the first 100 natural numbers is a composite number is ? 
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 5 / 2
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: there are 6 different travelers who each have a choice of vacationing at one of 10 different destinations . what is the probability that all 6 travelers will end up vacationing at the same destination ? 
Options: a ) 0.1 , b ) 0.001 , c ) 0.0002 , d ) 1.0 e - 05 , e ) 0.0001
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 } , what is the probability that xy will be even ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a bag contains 2 white marbles and 2 black marbles . if each of 2 girls and 2 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? 
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
Output: 


Output: c
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 4 flips but not on the last flip ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32
Output: 


Output: e
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: what is the probability of getting a queen or spade from a set of cards ? 
Options: a ) 3 / 13 , b ) 4 / 13 , c ) 5 / 13 , d ) 6 / 13 , e ) 7 / 13
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ? 
Options: a ) 1 / 16 , b ) 5 / 16 , c ) 2 / 5 , d ) 13 / 16 , e ) 27 / 32
Output: 


Output: d
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 45 is a prime number , when each of the given numbers is equally likely to be selected ? 
Options: a ) 10 / 45 , b ) 14 / 45 , c ) 8 / 45 , d ) 3 / 45 , e ) 7 / 45
Output: 


Output: b
Definition: In this task, you need to provide the correct option for a given problem on probability from the provided options.

Positive Example 1 -
Input: Problem: in a throw of a coin find the probability of getting a tail ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Output: a

Positive Example 2 -
Input: Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e

Negative Example 1 -
Input: Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Output: b

Negative Example 2 -
Input: Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480
Output: a

Now complete the following example -
Input: Problem: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is 
Options: a ) 7 / 19 , b ) 6 / 19 , c ) 5 / 19 , d ) 4 / 19 , e ) none of these
Output: 


Output: a