What is the probability that a family with three children will have: a) All boys? 1/8 b) One girl? c) Two girls?
What is the probability that a family with three children will have: a) All boys? 1/8 b) One girl? c) Two girls?
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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![### Probability of Gender Combinations in a Family with Three Children
When considering the probability of different gender combinations in a family with three children, the outcomes can be analyzed using basic principles of probability. Below are some questions to illustrate this concept:
**Question: What is the probability that a family with three children will have:**
1. **All boys?**
\[\text{Probability} = \frac{1}{8} \]
2. **One girl?**
\[ \_\_\_\_\_\_\_\_\_ \]
3. **Two girls?**
\[ \_\_\_\_\_\_\_\_\_ \]
To calculate these probabilities, consider the total possible outcomes when a family has three children. Each child can either be a boy (B) or a girl (G), and each combination is equally likely. The total number of possible combinations for three children is \(2^3 = 8\). These combinations are listed below:
1. BBB
2. BBG
3. BGB
4. BGG
5. GBB
6. GBG
7. GGB
8. GGG
From this, you can determine the probability for each specific question:
- **All boys (BBB):** There is only 1 such outcome out of 8, hence the probability is \(\frac{1}{8}\).
- **One girl:** Combinations that include exactly one girl are BBG, BGB, and GBB. There are 3 such outcomes out of 8, so the probability is \(\frac{3}{8}\).
- **Two girls:** Combinations that include exactly two girls are BGG, GBG, and GGB. There are 3 such outcomes out of 8, so the probability is \(\frac{3}{8}\).
### Diagrams/Graphs:
There are no diagrams or graphs in the provided text, but should there be any, they might illustrate the possible outcomes of children’s genders in a visual format, such as a tree diagram or a table enumerating all the possibilities.
For instance, a tree diagram would branch out from a starting point for each child, splitting into two branches at each node (one for boy and one for girl), until all 8 possible combinations are shown.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faed2933e-b67f-42a0-9fac-b6dce0e828b0%2F75262f3d-6286-48f1-9d37-b64bc99b1984%2Fyf6p3b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability of Gender Combinations in a Family with Three Children
When considering the probability of different gender combinations in a family with three children, the outcomes can be analyzed using basic principles of probability. Below are some questions to illustrate this concept:
**Question: What is the probability that a family with three children will have:**
1. **All boys?**
\[\text{Probability} = \frac{1}{8} \]
2. **One girl?**
\[ \_\_\_\_\_\_\_\_\_ \]
3. **Two girls?**
\[ \_\_\_\_\_\_\_\_\_ \]
To calculate these probabilities, consider the total possible outcomes when a family has three children. Each child can either be a boy (B) or a girl (G), and each combination is equally likely. The total number of possible combinations for three children is \(2^3 = 8\). These combinations are listed below:
1. BBB
2. BBG
3. BGB
4. BGG
5. GBB
6. GBG
7. GGB
8. GGG
From this, you can determine the probability for each specific question:
- **All boys (BBB):** There is only 1 such outcome out of 8, hence the probability is \(\frac{1}{8}\).
- **One girl:** Combinations that include exactly one girl are BBG, BGB, and GBB. There are 3 such outcomes out of 8, so the probability is \(\frac{3}{8}\).
- **Two girls:** Combinations that include exactly two girls are BGG, GBG, and GGB. There are 3 such outcomes out of 8, so the probability is \(\frac{3}{8}\).
### Diagrams/Graphs:
There are no diagrams or graphs in the provided text, but should there be any, they might illustrate the possible outcomes of children’s genders in a visual format, such as a tree diagram or a table enumerating all the possibilities.
For instance, a tree diagram would branch out from a starting point for each child, splitting into two branches at each node (one for boy and one for girl), until all 8 possible combinations are shown.
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