A couple plans to have 7 children. Find the probability of having at least one girl
Question
A couple plans to have 7 children. Find the probability of having at least one girl.
Solution
To solve this problem, we will use the concept of probability.
Step 1: Identify the total number of outcomes The couple plans to have 7 children, and each child can be either a boy or a girl. So, for each child, there are 2 possibilities. Therefore, the total number of outcomes is 2^7 = 128.
Step 2: Identify the favorable outcomes The favorable outcomes are the cases where there is at least one girl. The only case that is not favorable is when all children are boys. There is only 1 such case.
Step 3: Calculate the probability The probability of an event is the number of favorable outcomes divided by the total number of outcomes. In this case, the probability of having at least one girl is (128 - 1) / 128 = 127 / 128 = 0.9921875.
So, the probability of the couple having at least one girl among their 7 children is approximately 0.992 or 99.2%.
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