Question

Let e be the event that a grad student is enrolled in an economics course, and s be the event that a grad student is enrolled in a statistics course. It is known that 40% of all grad students are enrolled in an economics course and 35% are enrolled in statistics, with 15% enrolled in both. Find the probability that a grad student is in economics and is also in statistics.

a) 20%
b) 25%
c) 15%
d) 10%

Answer 1

The probability that a grad student is enrolled in both an economics course and a statistics course is given as 15%, which is option c).

Step-by-step explanation:

The probability that a grad student is enrolled in both an economics course and a statistics course can be determined using the principle of inclusion-exclusion for probabilities. The formula to find the probability of the union of two events (in this case, being enrolled in economics and statistics) is P(e ∪ s) = P(e) + P(s) - P(e ∩ s), where P(e) is the probability of being enrolled in economics, P(s) is the probability of being enrolled in statistics, and P(e ∩ s) is the probability of being enrolled in both.

In the given question, we know that P(e) = 40%, P(s) = 35%, and P(e ∩ s) = 15%. Applying these values to the formula gives us:

P(e ∪ s) = 40% + 35% - 15% = 60%.

However, the question specifically asks for P(e ∩ s), which is the probability of a grad student being enrolled in both an economics and a statistics course. This is directly given as 15%, which corresponds to option c).