Solve the problem.
-Suppose that a family has 5 children and that the probability of having a girl is 12 . What is the probability of having exactly two girls and three boys?
A) 0.0625
B) 0.0312
C) 0.3125
D) 0.6252

Question

Quizplus · Accepted Answer

The probability of having exactly two girls and three boys can be calculated using the binomial probability formula, which is $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n$ is the total number of trials (children, in this case, which is 5), $k$ is the number of successful outcomes (having 2 girls), $p$ is the probability of success on each trial (having a girl, which is 1/2), and $1-p$ is the probability of failure (having a boy, also 1/2 in this case). Plugging in the values, we get $P(2 \text{ girls}) = \binom{5}{2}(1/2)^2(1/2)^{5-2} = 10 \cdot (1/4) \cdot (1/8) = 10/32 = 0.3125$.

Solve the Problem. -Suppose That a Family Has 5 Children and That the and That