Assume 75% of the AP stats students studied for this

dohtarjev510

dohtarjev510

Answered question

2022-02-12

Assume 75% of the AP stats students studied for this test. If 40% of those who studied get an A but only 10% of those who did not study get A, what is the probability that someone who gets an A actually studied for the test?

Answer & Explanation

Veschettijib

Veschettijib

Beginner2022-02-13Added 12 answers

The probability is (approximately) 92.31%.
Explanation:
Let A be the event that the student got an A on the test.
Let B be the event that the student studied.
It sounds like we are seeking the conditional probability of, "studied for the test GIVEN THAT they got an A".
This is written as P(BA), and it is read as "probability of B given A."
We are told:
P(B)=0.75 which means P(BC)=0.25
P(AB)=0.4
P(ABC)=0.1
(the C means "complement")
and we want to find P(BA). By definition,
P(BA)=P(BA)P(A)
Using Bayes
Vaughn Bradley

Vaughn Bradley

Beginner2022-02-14Added 16 answers

Let A= the student get an A in test
Let B= the student studied for test
We know that P(B)=0.75 and P(AB)=0.40
We know also that P(AB)=P(AB)P(B)=0.40
We are looking for P(AB)=0.40×0.75=0.3

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