Question

A recent survey found that 65% of high school students were currently enrolled in a math class, 43% were currently enrolled in a science class, and 13% were enrolled in both a math and a science class. Suppose a high school student who is enrolled in a math class is selected at random. What is the probability that the student is also enrolled in a science class?
0.20
0.28
0.30
0.66

Answer 1

Two triangles are similar. Triangle ABC has side lengths of AB = 10, BC = 6, CA = 7. Triangle XYZ has a side length of XY = 8.

Answer 2

Answer: Choice A)  0.20

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Explanation:

Let's say there are 1000 students. The students must take math, science or they can take both simultaneously.

• 65% of them are in math. So there are 0.65*1000 = 650 math students.
• 43% are in science, leading to 0.43*1000 = 430 science students.
• 13% are in both so we have 0.13*1000 = 130 students who are in both.

Now onto the sentence that says "Suppose a high school student who is enrolled in a math class is selected at random"

This means we only focus on the 650 math students and ignore the 1000-650 = 350 students who aren't in math.

Of those 650 math students, 130 are also in science (since 130 are in both classes).

The probability we're after is therefore 130/650 = 0.20