Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with five children will have at least one boy.
probability of no boys = .5^5
so probability of one or more than 1
= 1 - .5^5
= .969
To find the probability that a family with five children will have at least one boy, we can determine the probability of the complementary event: the probability that a family with five children will have all girls.
The probability of having a girl in any birth is 0.5, which means the probability of having a boy is also 0.5. Since each child's birth is independent, we can calculate the probability of having all girls by multiplying these probabilities together:
P(all girls) = (0.5) * (0.5) * (0.5) * (0.5) * (0.5) = 0.03125 (or 1/32)
Now, the probability of having at least one boy is equal to 1 - P(all girls) since having at least one boy is the complementary event of having all girls. Thus,
P(at least one boy) = 1 - P(all girls) = 1 - 0.03125 = 0.96875 (or 31/32)
Therefore, the probability that a family with five children will have at least one boy is 0.96875 or 31/32.