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 exactly three girls and two boys?
A) 0.6252
B) 0.3125
C) 0.0313
D) 0.0625

Question

Quizplus · Accepted Answer

The probability of having exactly three girls and two boys in a family of five children, where each child is equally likely to be a boy or a girl, can be calculated using the binomial probability formula. The formula for exactly k successes (in this case, girls) out of n trials (children) is $P(k; n, p) = \binom{n}{k}p^k(1-p)^{n-k}$, where $p$ is the probability of success (having a girl) on each trial. Here, $n=5$, $k=3$, and $p=\frac{1}{2}$. Thus, the probability is $\binom{5}{3}\left(\frac{1}{2}\right)^3\left(\frac{1}{2}\right)^{5-3} = 10\left(\frac{1}{32}\right) = \frac{10}{32} = 0.3125$.

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

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