Question

A psychology class consists of 14 males and 36 females. if the professor selects names from the class list using random sampling, what is the probability that the first student selected will be a female? if a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male?

Answer 1

The probability of selecting a female student for the first picking is $\frac{36}{50} = \frac{18}{25}$
The number of students left to select from after the first two students selected is 50 - 2 = 48 students, which consist of 34 females (two have been selected) and 14 males (none has been selected so far)
The probability that the third pick is a male is $\frac{14}{48}= \frac{7}{24}$