Question

A class consists of 10 males and 30 females. A random sample of n = 3 students is selected. If the first two students are both females, what is the probability that the third student is a male?

a. 10/37

b. 10/38

c. 10/40

d. 8/38

Answer 1

The probability that the third student selected from a class, after two females have already been chosen, is a male is 10/38. This is calculated by dividing the number of remaining males (10) by the total number of students left to choose from (38).

Step-by-step explanation:

If the first two students selected from the class are both females, the remaining class composition would be 28 females and 10 males, as the two females are no longer in the pool of potential students to be selected. We are interested in the probability that the third student is a male.

Since the selection is random, each student still in the class has an equal chance of being selected as the third student. So, the probability that the third student is a male is calculated by dividing the number of males by the total number of students still available.

The calculation is as follows:

• Number of males left: 10
• Total number of students left: 28 females + 10 males = 38 students
• Probability that the third student is a male: 10 males / 38 students

Therefore, the probability that the third student is male is 10/38.