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What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter
your answer as a decimal to the ten thousandths place.

What is the probability that a student took AP Chemistry given they did not get into their firstchoice college Enter your answer as a decimal to the ten thousan class=

Respuesta :

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

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] 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:

[tex]P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605[/tex]

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

Then, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273[/tex]

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 https://brainly.com/question/14398287

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