instruction:
In this task, you need to provide the correct option for a given problem on probability from the provided options.
question:
Problem: there are 4 books on a shelf , of which 3 are paperbacks and 6 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 111
answer:
e

question:
Problem: denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination .
Options: a ) 1 , b ) 159 / 160 , c ) 157 / 160 , d ) 4 3 / 160 , e ) 0
answer:
c

question:
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 z that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
answer:
d