In the United​ States, the true probability of a baby being male is 0.5119. For a family having four ​children, find the probabilities ; the probability that all four children are male 

The problem is asking for the probability that all four children in a family are male, given that the probability of a baby being male is 0.5119. We can use the basic rules of probability to solve this.

Since each child is independent of the others, the probability that all four children are male is the product of the individual probabilities for each child:

\[
P(\text{all four male}) = 0.5119 \times 0.5119 \times 0.5119 \times 0.5119
\]

This can be written as:

\[
P(\text{all four male}) = (0.5119)^4
\]

Now, let's compute this.

\[
P(\text{all four male}) = 0.5119^4 \approx 0.0686
\]

So, the probability that all four children are male is approximately **0.0686**, or **6.86%**.

### Do you want details or have any questions?

Here are five related questions for further exploration:
1. What is the probability that all four children are female?
2. What is the probability that exactly three children are male?
3. What is the probability that at least one child is male?
4. How would the probability change if the family had five children?
5. What if the probability of a child being male were different in another country—how would that affect the outcome?

**Tip:** When working with probabilities of independent events, always multiply the individual probabilities together.

In the United States, the true probability of a baby being male is 0.5119. For a family having four children, find the probability that all four children are male.

Learn how to calculate the probability of all four children being male in a family where the probability of a baby being male is 0.5119. This problem covers fundamental probability concepts, including independent events and multiplication rules, suitable for students in Grades 9-12.

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