Assume that boys and girls are equally likely. Find the probability that when a couple has three children, there are exactly 0 boys.
What is the probability of exactly 0 boys out of three children?
(Type an integer or a simplified fraction.)
Answer
Final Answer: The probability of a couple having three girls (and therefore 0 boys) when they have three children is \(\boxed{\frac{1}{8}}\) or 0.125.
Step 1 ：Assume that boys and girls are equally likely. The probability of having a boy or a girl is \(\frac{1}{2}\).
Step 2 ：When a couple has three children, we need to calculate the probability of having a girl three times in a row.
Step 3 ：This is a simple multiplication of probabilities, because the events are independent (the gender of one child does not affect the gender of the other children).
Step 4 ：So, the probability of having three girls is \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}\) or 0.125.
Step 5 ：Final Answer: The probability of a couple having three girls (and therefore 0 boys) when they have three children is \(\boxed{\frac{1}{8}}\) or 0.125.
