Question

section 5.3 homework score: 10/13 answered: 10/13 question 11 a couple plans to have three children. what is the probability that a) they have all girls? b) they have at least one boy?

Explanation:

Step1: Determine the probability of each child being a girl

The probability of a child being a girl is $\frac{1}{2}$.

Step2: Calculate the probability of having all - girls for three - children

Since the events of having a girl for each child are independent, we use the multiplication rule for independent events. The probability of having all girls for three children is $P(\text{all girls})=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Step3: Calculate the probability of having at least one boy

The probability of having at least one boy is the complement of the event of having all girls. Let $A$ be the event of having at least one boy and $B$ be the event of having all girls. Then $P(A) = 1 - P(B)$. Since $P(B)=\frac{1}{8}$, then $P(A)=1-\frac{1}{8}=\frac{7}{8}$.

Answer:

a) $\frac{1}{8}$
b) $\frac{7}{8}$