The Martinos plan to have ten children. a) Determine the probability that all their children will be boys. (Assume that $P\left(\right.$ boy) $=\frac{1}{2}$ and assume independence.) b) If their first nine children are boys and Mrs. Martino is expecting another child, what is the probability that the tenth child will be a boy? a) The probability that all their children will be boys is $\square$. (Type an integer or a simplified fraction.)

Step 1 ：The Martinos plan to have ten children. We are asked to determine the probability that all their children will be boys. We assume that the probability of having a boy is \( \frac{1}{2} \) and that each birth is independent of the others.

Step 2 ：The probability of having a boy is \( \frac{1}{2} \). Since each birth is independent, the probability of having ten boys in a row is \( \left(\frac{1}{2}\right)^{10} \).

Step 3 ：Calculating \( \left(\frac{1}{2}\right)^{10} \) gives us a probability of 0.0009765625.

Step 4 ：Final Answer: The probability that all their children will be boys is \( \boxed{0.0009765625} \).

Step 5 ：If their first nine children are boys and Mrs. Martino is expecting another child, we are asked to determine the probability that the tenth child will be a boy.

Step 6 ：Since each birth is independent, the probability that the tenth child will be a boy is still \( \frac{1}{2} \).