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murzikaleks [220]
3 years ago
15

Billy takes two tests in his probability and statistics class. The probability that Billy would pass at least one test is 0.9. T

he probability that he passes both tests is 0.7. The tests are of equal difficulty (that is, the probability that Billy passes test 1 is the same as the probability that he passes test 2.)
What is the conditional probability of Billy passing test 2 given the event that he passes test 1?
Mathematics
1 answer:
scZoUnD [109]3 years ago
6 0

Answer:

0.875 is the required probability.                                

Step-by-step explanation:

We are given the following in the question:

Probability Billy would pass atleast one test = 0.9

P(A\cup B) = 0.9

Probability Billy would pass both test = 0.7

P(A\cap B) = 0.7

The two test are equally difficult.

P(A) = P(B)

For independent events we can write that

P(A\cup B) = P(A) + P(B) -P(A\cap B)\\0.9 = 2P(A) - 0.7\\2P(A) = 1.6\\P(A) = P(B)=0.8

We have to find the conditional probability that Billy passing test 2 given the event that he passes test 1.

P(B|A) = \dfrac{P(B\cap A)}{P(A)} = \dfrac{0.7}{0.8} = 0.875

0.875 is the conditional probability of Billy passing test 2 given the event that he passes test 1

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