Question

If 40 people are called to be on a jury in a group of 25 men and 15 women, what is the probability that the first two people called are both women?

A) 3/8
B) 1/3
C) 7/40
D) 1/2

Answer 1

The probability that the first two people called are both women from a group of 40 people (25 men and 15 women) is 3/8, calculated by multiplying the two sequential probabilities of picking a woman without replacement.

Step-by-step explanation:

The student is asking about the probability that the first two people called are both women from a group of 25 men and 15 women. To solve this, you calculate the probability of selecting a woman two times in a row without replacement.

For the first woman, the probability is 15/40 since there are 15 women out of 40 people. Once the first woman is selected, there are now 14 women left and 39 people in total. So, the probability of selecting another woman is 14/39.

To find the probability that both events occur in sequence, you multiply the probabilities of each event: 15/40 * 14/39, which simplifies to 3/8.

Thus, the correct answer is A) 3/8.