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Your friend is studying for an exam. Based on your knowledge of your friend, you believe that if they study for the exam, there is an 80% probability they will be able to pass it. On the other hand, if they do not study, there is only a 30% probability they will be able to pass. Your friend is not a particularly industrious student, and you initially believe there is only a 60% probability your friend will study for the exam. A few days later your friend happily proclaims that they passed the exam. Thus, find the probability that they did in fact study for the test with this knowledge in hand.

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Answer:

0.8 = 80% probability that they did in fact study for the test.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is


P(B|A) = (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 question:

Event A: Passed the exam.

Event B: Studied.

Probability of passing the test:

80% of 60%(Studied).

30% of 100 - 60 = 40%(did not study). So


P(A) = 0.8*0.6 + 0.3*0.4 = 0.6

Probability of passing the test studying:

80% of 60%, so:


P(A \cap B) = 0.8*0.6 = 0.48

Find the probability that they did in fact study for the test with this knowledge in hand.


P(B|A) = (P(A \cap B))/(P(A)) = (0.48)/(0.6) = 0.8

0.8 = 80% probability that they did in fact study for the test.

User Kyo Dralliam
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