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A couple plans on having three children. Suppose that the probability of any given child being female is​ 0.5, and also suppose that the genders of each child are independent events. a. Write out all outcomes in the sample space for the genders of the three children. b. What should be the probability associated with each​ outcome? c. Using the sample space constructed in part​ a, find the probability that the couple will have three boys. d. Using the sample space constructed in part​ a, find the probability that the couple will have at least one child of each gender.

Answer :

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Answer:

a. S={BBB, BBG, BGB, BGG, GGG, GGB, GBG, GBB}

b. 0.125 or 12.5%

c. 0.125 or 12.5%

d. c. 0.75 or 75%

Step-by-step explanation:

Let B represent a boy being born, and G represent a girl being born.

a. The sample space for three children is:

S={BBB, BBG, BGB, BGG, GGG, GGB, GBG, GBB}

b. Since each outcome is equally likely and there are 8 possible outcomes, the probability of each outcome is:

[tex]P=\frac{1}{8}=0.125=12.5\%[/tex]

c. In only one outcome the couple will have three boys (BBB). Therefore, the probability is 0.125 or 12.5%.

d. In only two outcomes, the couple will NOT have at least one child of each gender (BBB and GGG). Therefore, the probability is:

[tex]P=1-(2*0.125)=0.75=75\%[/tex]

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