Problem

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.)

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/17936/

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