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 box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ? 
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
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 bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turnon to be white , if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ? 
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 3 / 8 , e ) 4 / 9
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: jane and thomas are among the 7 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ? 
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
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: 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 / 8 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? 
Options: a ) 134 , 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: there are 23 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 1254 , b ) 1482 , c ) 1771 , d ) 1875 , e ) 1923
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: 6 animals of a circus has to be placed inside in 6 cages one in each cage . if 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal . 
Options: a ) a . 240 , b ) b . 808250 , c ) c . 502450 , d ) d . 784200 , e ) e . 302400
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: in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate . 
Options: a ) 144 , b ) 288 , c ) 12 , d ) 576 , e ) none
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: when two dice are tossed , what is the probability that the total score is a prime number ? 
Options: a ) 1 / 6 , b ) 3 , c ) 5 / 12 , d ) 7 / 12 , e ) 9 / 12
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: a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ? 
Options: a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38
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: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn . 
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these
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: in how many ways can 21 books on english and 19 books on hindi be placed in a row on a shelf so that two books on hindi may not be together ? 
Options: a ) 1540 , b ) 2314 , c ) 5420 , d ) 1240 , e ) 4512
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: when two dice are rolled , what is the probability that the sum is either 7 or 11 ? 
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 4 / 3 , d ) 3 / 9 , e ) 2 / 9
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: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 5 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight 
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 2 / 5 , d ) 3 / 4 , e ) 7 / 8
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 main line train starts at 5.00 am and the harbor line train starts at 5.02 am . each train has the frequency of 10 minutes . if a guy goes in the morning at a random time what is the probability of he getting main line train ? 
Options: a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8
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: 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 y 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: the chance of rain on any given day in tel - aviv is 50 % . what is the probability e that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? 
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Output: 


Output: a