Question

given a family with three children, find the probability of the event.
all are boys.

the probability that all of the children are boys is □.
(simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Determine total possible outcomes

Each child can be a boy (B) or a girl (G). For 3 children, the total number of possible outcomes is $2\times2\times2 = 2^3 = 8$. The sample space is {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}.

Step2: Determine favorable outcomes

The event "all are boys" has only 1 favorable outcome: BBB.

Step3: Calculate probability

Probability is the number of favorable outcomes divided by the number of total outcomes. So, $P(\text{all boys}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} = \frac{1}{8}$.

Answer:

$\frac{1}{8}$