Final answer:
The probability that a couple has at least one girl is 1 minus the probability of having all boys. For one child, this probability is 50%. For two children, it would be 75%.
Step-by-step explanation:
To find the probability that when a couple has children, at least one of them is a girl, we will use the concept of complementary events. The only way for the event 'at least one child is a girl' to fail is if all the children are boys. Assuming that the probability of having a boy or a girl is equal (50% each), and considering the simplest scenario of one child, the probability of having a boy (B) is 0.5. Therefore, the probability of having at least one girl (G) is 1 minus the probability of not having a girl (all boys), which is:
P(G) = 1 - P(B)
P(G) = 1 - 0.5
P(G) = 0.5 or 50%
For multiple children, we would raise the individual probability to the power of the number of children (n). Let's say for two children, the probability of having two boys (BB) is (0.5)^2, hence the probability of at least one girl is:
P(at least one G) = 1 - P(BB)
P(at least one G) = 1 - (0.5)^2
P(at least one G) = 1 - 0.25
P(at least one G) = 0.75 or 75%