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Asked Jan 9, 2020
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Calculus Pretest. Students are given three chances to pass a basic skills exam for permission to enroll in Calculus I. Sixty percent of the students pass on the first try; of those that fail on the first try, 54% pass on the second try; and of those remaining, 48% pass on the third try.

a. What is the probability that a student passes on the second try?
b. What is the probability that a student passes on the third try?
c. What percentage of students pass?

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Expert Answer

Step 1

Given that,

Sixty percent of the students pass on the first try; of those that fail on the first try, 54% pass on the second try; and of those remaining, 48% pass on the third try.

Step 2

a)

Let A denote that the selected student fail on the first try and B denotes that the selected student passes on the second try.

That is 40% of the students failed on the first try.

P (A) =40%

P (B) = 54%

The probability that a student passes on the second try is 0.216.

Statistics homework question answer, step 2, image 1
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Step 3

b)

Let A denote that the selected student fail on the first try and B denotes that the selected student passes on the second try.

That is 40% of the students failed on the first try.

That is 46% of the students passes on the second try.

Then 48% of the students passes on the third try.

The probability that a student passes on the third try is 0.088.

...
Statistics homework question answer, step 3, image 1
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