Question

We will now find the probability that at least one child is a female. The problem asks us to notice that the complement of the event "all three children are male" is "at least one of the children is female." Recall that the probability of the complement of an event is given by 1 − P(event). Therefore, the probability that at least one child is a female can be calculated using the following formula. P(at least one child is female) = 1 − P(all three children are male) We previously determined that P(all three children are male) = 1 8 . Applying this value to the formula allows us to calculate the probability that at least one child is a female. Enter your probability as a fraction. P(at least one child is female) = 1 − P(all three child

Answer 1

Answer:

$\displaystyle \frac{7}{8}$.

Step-by-step explanation:

If two events are complements, then the sum of their probabilities should be $1$.

This question suggests that the following two events are complements:

• At least one child is female.
• All three children are male.

As a result:

$\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male})\end{aligned}$.

According to the question,

$\displaystyle P(\text{all three children are male}) = \frac{1}{8}$.

Therefore,

$\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male}) \\ &= 1 -\frac{1}{8} \\ &= \frac{7}{8}\end{aligned}$.