The Jones family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had: at least 3 girls? at most 5 girls?
The Jones family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had: at least 3 girls? at most 5 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 in Large Families
The Jones family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Jones family had:
- **At least 3 girls:** [ ]
- **At most 5 girls:** [ ]
### Additional Instructions
Calculate the respective probabilities for the scenarios and enter your answers in the boxes provided.
#### Example Calculation:
For a family with 7 children, the probability of exactly 3 girls can be calculated using the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]
Where:
- \( n \) is the total number of trials (in this case children, so \( n = 7 \))
- \( k \) is the number of successful trials (in this scenario, the number of girls)
- \( p \) is the probability of success on a single trial (the probability of being a girl, so \( p = 0.5 \))
Ensure to sum the probabilities appropriately for "at least" and "at most" scenarios.
When ready, click the "Next Question" button to proceed to the next problem.
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Transcribed Image Text:## Probability in Large Families
The Jones family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Jones family had:
- **At least 3 girls:** [ ]
- **At most 5 girls:** [ ]
### Additional Instructions
Calculate the respective probabilities for the scenarios and enter your answers in the boxes provided.
#### Example Calculation:
For a family with 7 children, the probability of exactly 3 girls can be calculated using the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]
Where:
- \( n \) is the total number of trials (in this case children, so \( n = 7 \))
- \( k \) is the number of successful trials (in this scenario, the number of girls)
- \( p \) is the probability of success on a single trial (the probability of being a girl, so \( p = 0.5 \))
Ensure to sum the probabilities appropriately for "at least" and "at most" scenarios.
When ready, click the "Next Question" button to proceed to the next problem.
[Next Question]
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