In a certain country, the true probability of a baby being a boy is 0.537. Among the next five randomly selected births in the country, what is the probability that at least one of them is a girl?
The probability is
(Round to three decimal places as needed.)

To solve this problem, we need to use the concept of complementary probability.

### Step 1: Find the probability of having all boys.
The probability that a baby is a boy is given as \( P(\text{Boy}) = 0.537 \).

The probability that all 5 babies are boys is:
\[
P(\text{All 5 boys}) = (0.537)^5
\]

Let's calculate that value.

### Step 2: Use the complementary probability to find at least one girl
The probability that there is at least one girl is the complement of all 5 being boys:
\[
P(\text{At least one girl}) = 1 - P(\text{All 5 boys})
\]

Now let's calculate this probability.The probability that at least one of the next five randomly selected births will be a girl is **0.955**.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

1. What is the probability that all five babies are girls?
2. What is the probability that exactly three out of the five babies will be boys?
3. How would the probability change if the probability of a boy were different?
4. What is the probability that at least two of the five babies will be girls?
5. How would the approach differ if we wanted the probability of having at most one girl?

**Tip:** Complementary probability is a powerful technique that simplifies finding the likelihood of "at least one" occurrences in a scenario.

In a certain country, the true probability of a baby being a boy is 0.537. Among the next five randomly selected births in the country, what is the probability that at least one of them is a girl?

Calculate the probability that at least one of five randomly selected births will be a girl when the probability of a baby being a boy is 0.537. This problem explores complementary probability and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation