SOLUTION: If a couple has three children, what is the probability that they have at least one boy.

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Question 425908: If a couple has three children, what is the probability that they have at least one boy.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the probability of at least a boy is 1 minus the probability of no boys.

the probability that each child will be a boy is 1/2.
the probability that each child will be a girl is 1/2.

the probability of no boys = 1/2 * 1/2 * 1/2 = 1/8

the probability of at least 1 boy is 1 minus the probability of no boys.

this equals 1 - 1/8 = 7/8

the breakdown of the possibilities is shown below:

probability of 0 boys = 1/8
probability of 1 boy = 3 * 1/8 = 3/8
probability of 2 boys = 3 * 1/8 = 3/8
probability of 3 boys = 1/8

total probability should be equal to 1.

1/8 + 3/8 + 3/8 + 1/8 = 1

you can see from this that the probability of at least 1 boy is equal to the probability of 1 or 2 or 3 boys which equals 3/8 + 3/8 + 1/8 = 7/8

this is the same as 1 minus the probability of 0 boys.