Question
Asked Sep 22, 2019
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Assuming that boy and girl babies are equally likely, find the probability that a family with
three children has all boys given that the first two are boys.
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Assuming that boy and girl babies are equally likely, find the probability that a family with three children has all boys given that the first two are boys.

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Expert Answer

Step 1

Conditional rule:

The formula for probability of A given B is,

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P(A| B)=PA and B) Р(В) P(A and B)

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Step 2

It is given that the family has three children and possibility of boy and girl are equally likely. Thus, the sample space consists of 8 elements with equally likely probability, 1/8 and is given below:

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S BBB,GGG,BGB,GBB,BBG,GBG,GGB,BGG

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Step 3

Finding the probability that a family with three children has all boys given that the first two are boys:

The probability that a fa...

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P(All boys and first two are boys) P(first two are boys) P(All boys first two are boys) P(All boys) P(first two are boys) = 2 =0.5

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