Quiz 4

3. 

If the sex of a child is independent of all other​ births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first​ birth? Explain.

Choose the correct answer below.

1. Yes, the probability after having four boys is greater than the probability on her first birth. Since the empirical probability after having four boys is 0 and since the true probability cannot be​ 0, a girl must be more likely after having four boys.
2. No, the probability after having four boys is equal to the probability on her first birth. If sex is independent of previous​ births, then the probability of a girl given she has had four boys must equal the probability of a girl.
3. No, the probability after having four boys is less than the probability on her first birth. Because she has had four​ boys, the woman has been shown to be more likely to give birth to boys than girls.
4. Yes, the probability after having four boys is greater than the probability on her first birth. By the Law of​ Averages, she is due to give birth to a girl after having four​ boys, since the​ long-run probability of a girl is 0.5.