Question

Given eight students, three of whom are female, if two students are selected at random without replacement, what is the probability that both students are female?

Answer 1

The probability of selecting two female students at random without replacement from a group of eight students, three of whom are female, is 3/28 or approximately 0.1071.

Step-by-step explanation:

The question you have asked is about calculating the probability that both students selected at random from a group of eight students, three of whom are female, are female. To solve this, we use the concept of combinations and basic probability principles.

First, we calculate the probability of choosing one female student. There are 3 female students out of 8 total students, so the probability of choosing a female first is 3/8. After choosing one female student, there are now 7 students left and 2 female students left. The probability of choosing another female student is then 2/7. The probability of both events happening is the product of the two probabilities.

So, the probability of selecting two female students is:

(3/8) * (2/7) = 6/56 = 3/28 or approximately 0.1071.

This is how we can calculate the probability of selecting two female students at random without replacement from a group of eight students with three females.