Question 272098: In a family of three children there are 8 possibilities for the boy-girl combinations, such as BBG, GBG and so on.
a) The probability of all boys equals the probability of all girls. What would each of these be?
b) The probibility of 2 boys and 1 girl is equal to 3/8. Explain why it is 3/8 not 1/8.
c) For this family of three children, what other situation would have a probability equal to 3/8?
d) If the family had four children, how would the answer to part (a) change?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a family of three children there are 8 possibilities for the boy-girl combinations, such as BBG, GBG and so on.
a) The probability of all boys equals the probability of all girls. What would each of these be? (1/2)(1/2)(1/2) = 1/8
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b) The probability of 2 boys and 1 girl is equal to 3/8. Explain why it is 3/8 not 1/8.
The 1 girl may be the 1st with prob 1/8
Or she may be the 2nd with prob 1/8
Or she may be the 3rd with prob 1/8
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These three results are mutually exclusive so we have
to add the probability of each and get 3/8
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c) For this family of three children, what other situation would have a probability equal to 3/8?
P(2 girls) because it is the same as probability of one boy which equals (3/8)
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d) If the family had four children, how would the answer to part (a) change?
(1/2)(1/2)(1/2)(1/2) = 1/16
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Cheers,
Stan H.
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