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.) ....
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
Section: Chapter Questions
Problem 1P
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Question
![**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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c582252-6541-4096-9706-b4f3b52fcf1c%2F5130a437-cc7b-49ce-a35b-443b61d18ba6%2Ft6lbinq_processed.jpeg&w=3840&q=75)
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).
Expert Solution
Step 1
It is given that the probability of a baby being a boy is 0.514.
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