If a family plans to have four kids what is the probability that they will have at least one girl
Use the "back door" approach.
prob(all 4 boys) = (1/2)^4 = 1/16
We don't want that case
so prob(at least 1 girl in 4 kids) = 1 - 1/16 = 15/16
or
find prob(1 girl of 4) + prob(2 girls of 4) + prob(3 girls of 4) + prob(4 girls of 4)