Question

A couple plans to have children until they get a girl, but they agree they will not have more than three children, even if they are all boys. Assume that the probability of having a girl is 55% Find the expected number of girls they will have:

Answer 1

To find the expected number of girls a couple will have, we can use probability and expected value. By multiplying the probability of each outcome by the number of girls in that outcome, we can calculate the expected number of girls. In this case, the expected number of girls is 3.2.

Step-by-step explanation:

To find the expected number of girls the couple will have, we can use probability and expected value. Let's break it down:

1. There is a 55% chance of having a girl on each pregnancy attempt.
2. If the first child is a girl, they will have 1 girl in total.
3. If the first child is a boy, they will have 0 girls and will need to try for a second child.
4. If the second child is a girl, they will have 1 more girl, totaling 2 girls.
5. If the second child is a boy, they will have 0 girls and will need to try for a third child.
6. If the third child is a girl, they will have 1 more girl, totaling 3 girls.
7. If the third child is a boy, they will have 0 girls and their attempts will stop.

So, the possible outcomes are 0, 1, 2, or 3 girls. To find the expected number of girls, multiply the probability of each outcome by the number of girls in that outcome:

• Probability of 0 girls: 45% * 0 = 0
• Probability of 1 girl: 45% * 1 = 0.45
• Probability of 2 girls: 55% * 2 = 1.1
• Probability of 3 girls: 55% * 3 = 1.65

Add up the expected number of girls:

• 0 + 0.45 + 1.1 + 1.65 = 3.2

Therefore, the expected number of girls the couple will have is 3.2.