Question

There are 85 students enrolled in AVCS. Of those 85, 15 are taking probability and statistics, 10 are taking pre-calculus, and 5 are taking both. Find the probability that a student chosen at random is taking probability and statistics, given that he is taking pre-calculus.

Option 1: 1/2
Option 2: 1/3
Option 3: 1/4
Option 4: 1/5

Answer 1

The probability that a student chosen at random is taking probability and statistics, given that he is taking pre-calculus, is 1/2. Correct answer is Option 1: 1/2

Step-by-step explanation:

To find the probability that a student chosen at random is taking probability and statistics, given that he is taking pre-calculus, we need to use conditional probability. The conditional probability can be calculated using the formula:

P(A|B) = P(A∩B) / P(B)

where P(A|B) is the probability of event A given event B, P(A∩B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

In this case, event A is taking probability and statistics, and event B is taking pre-calculus.

We are given that 15 students are taking probability and statistics, 10 students are taking pre-calculus, and 5 students are taking both. Therefore, P(A∩B) = 5/85, P(B) = 10/85. Plugging these values into the formula, we get:

P(A|B) = (5/85) / (10/85) = 5/10 = 1/2

So the probability that a student chosen at random is taking probability and statistics, given that he is taking pre-calculus, is 1/2.