Question

An introductory psychology class has 30 male & 60 female freshmen, 14 male & 14 female sophomores, 12 male & 13 female juniors, and 6 male & 6 female seniors. Suppose that 26 students are to be randomly selected without replacement. If the first 10 students selected from the class were seniors, what is the probability that the next student will be a senior?

Answer 1

Dear student, please comment in the case of any doubt and I would love to clarify it.

P(A) = n(E)/n(S)

Where P(A) is the probability of an event A

n(E) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

We have a total of 90 freshmen(30 males and 60 females), 28 sophomores(14 males and 14 females), 25 juniors(12 males and 13 females), 12 seniors(6 males and 6 females).

If we have picked 10 seniors already, then only 2 seniors are left now.

The probability of the next student being a senior is 1 / (90 + 28 + 25 + 2) = 1/145

The probability of next student being senior is 1/145.