The multiplication rule. Here is another basic rule of probability: if several events are independent, the probability that all of the events happen is the product of their individual probabilities.We know, for example, that a child has probability 0.49 of being a girl and probability 0.51 of being a boy, and that the sexes of successive children are independent. So the probability that a couple’s two children are two girls is (0.49)(0.49) = 0.2401. You can use this multiplication rule to calculate the probability that we simulated in Example 4.

(a) Write down all 8 possible arrangements of the sexes of three children, for example, BBB and BBG. Use the multiplication rule to find the probability of each outcome. Check your work by verifying that your 8 probabilities add to 1.

(b) The couple in Example 4 plan to stop when they have a girl or to stop at 3 children even if all are boys. Use your work from

(a) to find the probability that they get a girl.

EXPLORING THE WEB