The table provides the probability distribution for the number of girls ($x$) out of 8 children, with each value of $P(x)$ corresponding to the probability of getting exactly $x$ girls.

Part (a): Find the probability of getting exactly 6 girls in 8 births.

From the provided table:

• $x = 6$
• $P(6) = 0.117$

Thus, the probability of getting exactly 6 girls in 8 births is:
$P(6) = 0.117$

So, the answer is:

0.117

Would you like me to walk through how these probabilities are calculated (using binomial distribution formulas)? Or do you have other questions related to this problem?

Here are 5 related questions:

1. What is the probability of getting at least 5 girls in 8 births?
2. What is the probability of getting no more than 4 girls?
3. How do you calculate the mean and standard deviation of a binomial distribution?
4. If the probability of a girl birth is 0.5, how would the probabilities change for each $x$?
5. How can cumulative probabilities be useful in interpreting this table?

Tip: In a binomial distribution, the sum of all individual probabilities $P(x)$ should always equal 1.