Question

Akili has two tests next week. The probability that he will pass the first test, science, is 3 4 . How he does on that test affects how he will do on his math test. If he passes science, then the probability that he will also pass the math test is 4 5 ; otherwise, the probability is only 1 3 that he will pass the math test. What is the probability he passes exactly one test

Answer 1

0.2333 = 23.33% probability he passes exactly one test

Explanation:

We have these following probabilities:

3/4 probability that he passes the first test.

If he passes the first test, 4/5 probability that he passes the math test.

If he does not pass the first test, 1/3 probability that he passes the math test.

What is the probability he passes exactly one test

Two scenarios:

Pass first(3/4 probability) and fails second(1/5 probability).

Fails first(1/4 probability) and passes second(1/3 probability). So

`p = (3)/(4)*(1)/(5) + (1)/(4)*(1)/(3) = (3)/(20) + (1)/(12) = (9 + 5)/(60) = (14)/(60) = 0.2333`

0.2333 = 23.33% probability he passes exactly one test