Question

a couple is thinking about having 3 children. assume that each child is equally likely to be a girl or a boy. what is the probability that exactly 2 of the children are girls? 0.125 0.25 0.375 0.5

Explanation:

Step1: Calculate the total number of possible outcomes

Each child has 2 possible genders (boy or girl). For 3 children, the total number of possible outcomes is \(2\times2\times2 = 2^{3}=8\) (using the multiplication principle for independent events).

Step2: Calculate the number of favorable outcomes

We use the binomial coefficient formula \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 3\) (number of children) and \(k=2\) (number of girls).

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The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (exactly 2 girls) is \(C(3,2) = 3\), and the total number of outcomes is \(8\). So \(P=\frac{3}{8}=0.375\)

Answer:

0.375