A couple has three children. Assuming independence and that the probability of a boy is 1/2, determine the probability that at least one child is a girl.
There are 8 possible outcomes when a couple has three children:
- BBB
- BBG
- BGB
- GBB
- BGG
- GBG
- GGB
- GGG
Out of these 8 outcomes, 7 have at least one girl. Thus, the probability that at least one child is a girl is 7/8 or 0.875.
To determine the probability that at least one child is a girl, we can use the concept of complementary probability.
First, let's consider the complement of the event "at least one child is a girl." In this case, the complement is "all children are boys."
The probability of a child being a boy is 1/2, so the probability of all three children being boys can be calculated as follows:
P(all boys) = (1/2) * (1/2) * (1/2) = 1/8.
Since we are considering the complement, we subtract this probability from 1:
P(at least one girl) = 1 - P(all boys) = 1 - 1/8 = 7/8.
Therefore, the probability that at least one child is a girl is 7/8.