Assume that births of babies born at a hospital are independent events, with the probability of a girl = 0.5 and the probability of a boy = 0.5 . What is the probability that of the next 3 babies born at the hospital, two of them are girls and one is a boy? (Note: the two girl and one boy babies can be born in any order.) Express your answer as a decimal value, rounded to three decimal places.
The correct answer is 0.375 . There are 8 different ways in which 3 babies can be born: GGG, GGB, GBG, BGG, BBG, BGB, GBB, and BBB. The probability of each of these eight ways is (.5)(.5)(.5) = .125. Notice that exactly three of the eight ways (GGB, GBG, and BGG) satisfy the requirement that two girls and one boy were born. Add these three probabilities together to get .375 .