In a certain country, the true probability of a baby being a boy is 0.514. Among the next four randomly selected births in the country, what is the probability tha least one of them is a girl? The probability is (Round to three decimal places as needed.) ....

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Problem Statement:**

In a certain country, the true probability of a baby being a boy is 0.514. Among the next four randomly selected births in the country, what is the probability that at least one of them is a girl?

---

**Solution:**

To find the probability that at least one of the four births is a girl, we can use the complementary probability. First, we calculate the probability that all four births are boys, and then subtract that probability from 1.

Given:
- Probability of a boy = 0.514
- Probability of a girl = 1 - 0.514 = 0.486

**Calculations:**

The probability that all four births are boys can be calculated as:
\[ P(\text{All boys}) = 0.514^4 \]

The probability that at least one birth is a girl is given by:
\[ P(\text{At least one girl}) = 1 - P(\text{All boys}) \]

After computing these probabilities, the answer should be rounded to three decimal places.

**Result:**

The probability is [__] (Round to three decimal places as needed).
Transcribed Image Text:**Problem Statement:** In a certain country, the true probability of a baby being a boy is 0.514. Among the next four randomly selected births in the country, what is the probability that at least one of them is a girl? --- **Solution:** To find the probability that at least one of the four births is a girl, we can use the complementary probability. First, we calculate the probability that all four births are boys, and then subtract that probability from 1. Given: - Probability of a boy = 0.514 - Probability of a girl = 1 - 0.514 = 0.486 **Calculations:** The probability that all four births are boys can be calculated as: \[ P(\text{All boys}) = 0.514^4 \] The probability that at least one birth is a girl is given by: \[ P(\text{At least one girl}) = 1 - P(\text{All boys}) \] After computing these probabilities, the answer should be rounded to three decimal places. **Result:** The probability is [__] (Round to three decimal places as needed).
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It is given that the probability of a baby being a boy is 0.514.

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