Mathematics: At a highschool, 90% of the students take Physics and 35% of the students take both Physics and Statistics. What is the probability that a student that is taking Physics is also taking Statistics?

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At a highschool, 90% of the students take Physics - id905653946, mohammadhosseinkarim

jhar9500

21.01.2022

38.89% probability that a student that is taking Physics is also taking Statistics

Step-by-step explanation:

We use the conditional probability formula to solve this question.

Suppose we have two events.

Event A and Event B.

The formula:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of B happening, given that A has happened.

$P(A \cap B)$ is the probability of these two events happening.

P(A) is the probability of A happening.

In this problem, we have that:

Event A: taking physics

Event B: taking statistics.

90% of the students take Physics

This means that P(A) = 0.9

35% of the students take both Physics and Statistics.

This means that $P(A \cap B) = 0.35$

What is the probability that a student that is taking Physics is also taking Statistics?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.35}{0.90} = 0.3889$

38.89% probability that a student that is taking Physics is also taking Statistics

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