16 percent of the customers of a mortgage company default on their payments. A sample of 5 customers is selected. What is the probability that exactly 2 customers in the sample will default on their payments? Answer:
16 percent of the customers of a mortgage company default on their payments. A sample of 5 customers is selected. What is the probability that exactly 2 customers in the sample will default on their payments? Answer:
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 Customer Default in Mortgage Payments**
*Question:*
16 percent of the customers of a mortgage company default on their payments. A sample of 5 customers is selected. What is the probability that exactly 2 customers in the sample will default on their payments?
[Answer: __________]
**Explanation:**
This problem can be addressed using the binomial probability formula, which is suitable for scenarios where there are a fixed number of independent trials, each result has two possible outcomes (default or not default), and the probability of success (default) remains constant.
The binomial probability formula is given by:
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]
Where:
- \( n \) is the number of trials (in this case, 5 customers)
- \( k \) is the number of successes we are interested in (in this case, 2 defaults)
- \( p \) is the probability of success (in this case, 0.16)
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \)
Using this formula, you can calculate the exact probability that 2 out of 5 customers will default on their mortgage payments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe12f3ad-f419-427a-9045-294545f74979%2Ff6498378-aab2-40bd-8230-284b1a818373%2Faxujis_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability of Customer Default in Mortgage Payments**
*Question:*
16 percent of the customers of a mortgage company default on their payments. A sample of 5 customers is selected. What is the probability that exactly 2 customers in the sample will default on their payments?
[Answer: __________]
**Explanation:**
This problem can be addressed using the binomial probability formula, which is suitable for scenarios where there are a fixed number of independent trials, each result has two possible outcomes (default or not default), and the probability of success (default) remains constant.
The binomial probability formula is given by:
\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]
Where:
- \( n \) is the number of trials (in this case, 5 customers)
- \( k \) is the number of successes we are interested in (in this case, 2 defaults)
- \( p \) is the probability of success (in this case, 0.16)
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \)
Using this formula, you can calculate the exact probability that 2 out of 5 customers will default on their mortgage payments.
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