Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with three children will have the given composition.A) Two boys and one girlB) at least one girlC) no girlsD) the two oldest children are girls

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Asked Nov 6, 2019
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Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with three children will have the given composition.

A) Two boys and one girl

B) at least one girl

C) no girls

D) the two oldest children are girls 

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Expert Answer

Step 1

Consider B represent a boy and G represents a girl. The total number of outcomes of 3 children in a family can be obtained as:

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

So, the total outcomes are 8.

a)   The total choices of two boys and one girl are GBB, BGB, BBG that is 3.

The required probability for 2 boys and one girl can be obtained as:

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Number of possible outcomes P(2 boys and 1 girl Total outcomes 3 =0.375

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Step 2

b)  The possible outcomes of at least one girl are GGG, GGB, GBG, GBB, BGG, BGB, BBG that is 7.

The required probability for at least one girl can be obtained as:

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Number of possible outcomes P(at least one girl): Total outcomes =0.875

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Step 3

c) The possible outcomes of no girl is BBB that is 1.

The req...

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Number of possible outcomes P(no girl)= Total outcomes 8 0.125

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