Questions: Quiz 2 Chapter 4 As always, show your work. 1) If a couple has three children, what is the probability that they have at least one girl?

Solution Steps

To find the probability that a couple with three children has at least one girl, we can use the complementary probability approach. First, calculate the probability of having no girls (i.e., all boys), and then subtract this probability from 1 to get the probability of having at least one girl.

To find the probability of having at least one girl, we first calculate the probability of having all boys. Assuming the probability of having a boy is \( \frac{1}{2} \), the probability of having three boys (and thus no girls) is: \[ P(\text{all boys}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]

The probability of having at least one girl is the complement of having all boys. Therefore, we subtract the probability of having all boys from 1: \[ P(\text{at least one girl}) = 1 - P(\text{all boys}) = 1 - \frac{1}{8} = \frac{7}{8} \]

Final Answer