Answer:
The easiest way to figure this is to find P(no girls in 5 births) = (1/2)^5 = 1/32 -------------- The P(at least one girl in 5 births) = 1 - 1/32 = 31/32
The probability that when they have five children, at least one of them is a boy is 31/32
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome:
The probability that a couple will have a boy or girl among the five children = 1/2
If they gave birth to 5 children:
The probability that when they have five children, at least one of them is a boy = 1 - (1/2)^n where:
n is the total number of children
The probability that when they have five children, at least one of them is a boy = 1 - (1/2)ⁿ
The probability that when they have five children, at least one of them is a boy = 1 - (1/2)⁵
The probability that when they have five children, at least one of them is a boy = 1- 1/32 = 31/32
Hence the probability that when they have five children, at least one of them is a boy is 31/32
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