Find the probability. Round to the nearest ten-thousandth when necessary.
-A family has five children. The probability of having a girl is 1/2. What is the probability of having Exactly 2 girls and 3 boys?
A) 0.0625
B) 0.0312
C) 0.6252
D) 0.3125

Question

Quizplus · Accepted Answer

The probability of having exactly 2 girls and 3 boys in a family of 5 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, having a girl) out of n trials (children) is given by $P(k; n, p) = \binom{n}{k}p^k(1-p)^{n-k}$, where $p$ is the probability of success (having a girl), $n$ is the total number of trials (children), and $k$ is the number of successes (girls) we're interested in. Here, $p = 1/2$, $n = 5$, and $k = 2$. Thus, the probability is $\binom{5}{2}(1/2)^2(1/2)^{5-2} = 10 \cdot (1/4) \cdot (1/8) = 10/32 = 0.3125$.

Find the Probability