Mathematics: At west high school, 16% of the student population is taking a calculus course, 11% is taking a physics course, and 4% is taking both. find the probability that a student chosen at random is taking a calculus course, given that the student is taking a physics course

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At west high school, 16% of the student population - id164559206, michealjackson2002

alyxxboothe

15.01.2022

The probability is:

$\dfrac{4}{11}$

Step-by-step explanation:

It is given that:

16% of the student population is taking a calculus course.

11% is taking a physics course.

and 4% is taking both.

Now we are asked to find the probability that the student is taking a calculus course given that he is taking physics course.

Let A denote the event of taking a calculus course.

B denote the event of taking a physics course.

A∩B denote the event of taking both.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

We know that:

$P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

From the information we have:

$P(A\bigcap B)=0.04$

P(B)=0.11

Hence,

$P(A|B)=\dfrac{0.04}{0.11}\\\\\\P(A|B)=\dfrac{4}{11}=0.3636$

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