Question

What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter

Answer 1

Using conditional probability, it is found that there is a 0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.

Conditional Probability

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

In which

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

• $P(A \cap B)$ is the probability of both A and B happening.

• P(A) is the probability of A happening.

In this problem:

• Event A: Did not get into their first-choice college.

• Event B: Took AP chemistry.

According to the chain given, the percentages associated with not getting into their first-choice college are:

• 0.1375(chemistry).

• 0.1575(physics).

• 0.24(Env Sci).

• 0.07(Biology).

Hence:

$P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605$

The probability of both not getting into their first-choice college and taking chemistry is 0.1375, hence $P(A \cap B) = 0.1375$

Then, the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273$

0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.

To learn more about conditional probability, you can take a look at brainly.com/question/14398287