Question

A professor teaches a very small class with only 4 students. One day, when returning a...

A professor teaches a very small class with only 4 students. One day, when returning a test, the professor simply shuffles the tests and hands each student one of the tests at random.

(Write all answers as fractions, not decimals) What is the probability all 4 students receive the correct test? ____

What is the probability that no one receives the correct test?______

What is the probability that one or more students receive the correct test?_____

Math   Statistics-And-Probability   
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Answer #1

a) Probability that all receive the correct test is computed here as:

= 1 / Total ways to distribute the test to 4 students

= 1 / 4!

= 1/24

Therefore 1/24 is the required probability here.

b) Probability that no one received the correct test is computed using derangement theorem here as:

Therefore 3/8 is the required probability here.

c) Probability that one or more students receive the correct test is computed here as:

= 1 - Probability that none receive the correct test

= 1 - (3/8)

= 5/8

Therefore 5/8 is the required probability here.

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