Question

There are 18 students in a group,15 of them passed math exam. 7 students from this group are chosen at random. Find a probability that less than 3 of them did not pass math exam.

Answer 1

Probability of number of students passed in a math exam is 15/18

That is p=15/18

In this case number of students choose at random is 7

that is n=7

here we want to calculate the probability that less than 3 of them did not pass the math exam

That is P(X<3)

Here X ~Binomial(n=7,p=.833)

so P(X<3)= P(X=2)+P(X=1)+P(X=0)

By solving this we get the answer as

                   =.0015776