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**a.** Find the probability of getting exactly 6 girls in 8 births.


To find the probability of getting exactly 6 girls in 8 births, we need to look at the corresponding value of \( P(x) \) when \( x = 6 \) in the provided table.

From the table:

- When \( x = 6 \) (the number of girls), \( P(x) = 0.107 \).

Thus, the probability of getting exactly 6 girls in 8 births is \( P(6) = 0.107 \).

Would you like a detailed explanation of how this table might have been constructed, or have any other questions? 

Here are 5 follow-up questions for further exploration:
1. What is the probability of getting at most 4 girls in 8 births?
2. What is the probability of getting at least 5 girls in 8 births?
3. How would you calculate the expected number of girls in 8 births using this table?
4. What is the probability of getting exactly 4 or exactly 6 girls in 8 births?
5. How would you compute the variance for the number of girls in this distribution?

**Tip:** The sum of all probabilities \( P(x) \) for \( x = 0 \) to \( x = 8 \) must equal 1 in a valid probability distribution. Always check this when dealing with such tables.

Find the probability of getting exactly 6 girls in 8 births.

Learn how to find the probability of getting exactly 6 girls in 8 births using a binomial probability distribution. The solution includes data from the probability table and explores core concepts of discrete probability.

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