Final answer:
The probability of exactly 9 boys being born out of ten births can be calculated using the binomial probability formula.
Step-by-step explanation:
The probability that exactly 9 boys are born out of ten births can be calculated using the binomial probability formula. The formula is:
P(x=k) = C(n, k) * p^k * q^(n-k)
where:
n is the number of trials/births,
k is the number of successful outcomes/boys,
p is the probability of success/boy,
q is the probability of failure/girl,
and C(n, k) is the combination of n and k.
In this case, n = 10, k = 9, p = 0.5, and q = 1 - p = 0.5.
Substituting the values into the formula:
P(x=9) = C(10,9) * 0.5^9 * 0.5^1 = 10 * 0.5^9 * 0.5^1 = 10 * 0.5^10 = 10 * 0.0009765625 = 0.009765625.
Therefore, the probability that exactly 9 boys are born out of ten births is approximately 0.0098.