Question

In a class, 25 students pursue science, 15 students pursue social studies, and 10 students pursue both. Find the probability that a student pursues social studies given that he/she pursues science.

Answer 1

The probability that a student pursues social studies given that he/she pursues science is calculated using conditional probability and is found to be 0.4 or 40%.

Step-by-step explanation:

To determine the probability that a student pursues social studies given that he/she pursues science, we need to apply the concept of conditional probability. The formula is P(A|B) = P(A AND B) / P(B), where P(A|B) is the probability of event A occurring given that event B has occurred.

In this case, event A is the event of a student pursuing social studies, and event B is the event of a student pursuing science. Given that 25 students pursue science (P(B)) and 10 students pursue both science and social studies (P(A AND B)), we can calculate the probability as follows:

P(A|B) = P(students pursue social studies | students pursue science) = P(A AND B) / P(B) = 10 / 25 = 0.4

Therefore, the probability that a student pursues social studies given that he/she pursues science is 0.4, or 40%.