ute probability for the following compound event. Assign a numerical value to the strength of the following argument: The Wilson fami

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Compute probability for the following compound event.
Assign a numerical value to the strength of the following argument:

The Wilson family has four children. Therefore, at least two of the children were born on the same day of the week.

Expert Solution
Step 1

Total days in a week = 7

Number of children in Wilson family  4

The probability that 1 child has born on any given day is calculated as:

P(1 child) = Total days / Total days in week = 7/7

Suppose 1st child is born on Monday, then total days left = 7-1 =6

The probability that 2nd child has born on any given day is calculated as:

P(2nd child) = Total days left / Total days in week = 6/7

Total days left = 7-2 =5

The probability that 3rd child has born on any given day is calculated as:

P(2nd child) = Total days left / Total days in week = 5/7

The probability that the 4th child has born on any given day is calculated as:

P(3rd child) = Total days left / Total days in week = 4/7

The probability that the four children born on different days is calculated as:

P=77×67×57×47=120343=0.3499

 

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