Question 425908
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.