Solve the problem.
-Suppose that a family has 5 children and that the probability of having a girl is $$\frac { 1 } { 2 } \text {. What is the }$$ probability of having no more than three boys?
A) 0.8125
B) 0.9688
C) 0.3125
D) 0.5000

Question

Quizplus · Accepted Answer

The probability of having no more than three boys includes the scenarios of having 0, 1, 2, or 3 boys. Since the probability of having a boy or a girl is 1/2 for each child, we can calculate the probability for each scenario and sum them up. The binomial probability formula is used here, which is P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time, p is the probability of success (having a boy in this case), and n is the total number of trials (children).- Probability of having 0 boys (5 girls): C(5, 0) * (1/2)^0 * (1/2)^5 = 1 * 1 * (1/32) = 1/32- Probability of having 1 boy: C(5, 1) * (1/2)^1 * (1/2)^4 = 5 * 1/2 * 1/16 = 5/32- Probability of having 2 boys: C(5, 2) * (1/2)^2 * (1/2)^3 = 10 * 1/4 * 1/8 = 10/32- Probability of having 3 boys: C(5, 3) * (1/2)^3 * (1/2)^2 = 10 * 1/8 * 1/4 = 10/32Adding these probabilities together: 1/32 + 5/32 + 10/32 + 10/32 = 26/32 = 0.8125.

Solve the Problem 12. What is the \frac { 1 } { 2 } \text {. What is the }21​. What is the

Solve the Problem $\frac { 1 } { 2 } \text {. What is the }$