Question

An Introductory management class has 30 male & 60 female freshmen, 12 male &14 female sophomares, 12 male & 13 female juniors, and 6 male & 6 female seniors. Suppose that 13 students ere to be randomly selected without replacement. If the first 8 students selected from the class were juniors, what is the probability that the next student will be a freshman? Submit Arswer Save Progress <<View Previous Question Question 12 of 13 View Next Question Home My Assignments Edenson Reques rey A 0 1207 AMSUNG

Answer 1

There are in total 90 freshmen, 26 sophomores, 25 juniors and 12 seniors.

13 students are to be randomly selected without replacement.

Let A denote the event that the first 8 students selected from the class were juniors

let B denote the even that the next student will be a freshman

then, Probability that given the first 8 students selected were from the class were juniors, the next student will be a freshman=

$P(B|A)=\frac{P(A \cap B)}{P(A)}$

$P(A \cap B)= \frac{25}{153}.\frac{24}{152}\frac{23}{151}\frac{22}{150}.\frac{21}{149}.\frac{20}{148}\frac{19}{147}.\frac{18}{146}.\frac{90}{145}$

$P(A)= \frac{25}{153}.\frac{24}{152}\frac{23}{151}\frac{22}{150}.\frac{21}{149}.\frac{20}{148}\frac{19}{147}.\frac{18}{146}$

$P(B|A)=\frac{90}{145} = 0.6206$