Final answer:
The probability that both of the randomly selected students are females, chosen with replacement from a class of 5 males and 7 females, is calculated using the multiplication rule and is found to be 49/144.
Step-by-step explanation:
The probability that both of the selected students are females from a statistics class that consists of 5 males and 7 females, with two students being randomly selected with replacement, can be calculated using the multiplication rule for independent events. Because we are sampling with replacement, the selection of one student does not affect the probability of selecting another student. Therefore, each selection is an independent event.
The probability of selecting a female student on the first draw is 7/12, since there are 7 females out of a total of 12 students. Since the selection is with replacement, the probability of selecting another female on the second draw remains 7/12. To find the probability of both events occurring, we apply the multiplication rule:
- P(First student is female) = 7/12
- P(Second student is female) = 7/12
- P(Both students are female) = P(First student is female) * P(Second student is female) = (7/12) * (7/12) = 49/144
Therefore, the probability that both selected students are females is 49/144.