According to the *Statistics Canada* website, the unemployment rate in Canada is approximately 8.0 % of the eligible workforce. 

If 20 members of the eligible workforce are randomly selected, what is the probability that exactly 3 of them are unemployed?

The probability is:    

This problem also involves a binomial distribution, where we want to find the probability of exactly 3 people being unemployed out of 20.

Given:
- \( n = 20 \) (number of trials or people selected),
- \( p = 0.08 \) (probability of unemployment),
- \( k = 3 \) (number of successes or unemployed individuals).

We use the binomial probability formula:

\[
P(X = 3) = \binom{20}{3} \cdot (0.08)^3 \cdot (0.92)^{17}
\]

Let's calculate this probability.The probability that exactly 3 out of 20 randomly selected members of the eligible workforce are unemployed is \( 0.141 \).

Would you like further details or have any questions?

---

**Related Questions:**

1. What is the probability that none of the 20 selected individuals are unemployed?
2. What is the expected number of unemployed individuals in a group of 20?
3. How does the probability change if we increase the selection size to 30?
4. What is the probability of finding at least 1 unemployed person in the group?
5. What is the probability that exactly 5 people are unemployed?
6. How would the probability change if the unemployment rate increased to 10%?
7. What is the standard deviation of the number of unemployed individuals in a sample of 20?
8. How would you calculate the probability of finding between 2 and 4 unemployed people?

**Tip:** When dealing with small probabilities like 8%, the binomial distribution can often be approximated by the Poisson distribution for larger sample sizes.

Learn how to calculate the probability of exactly 3 out of 20 randomly selected members of the eligible workforce being unemployed using the binomial distribution formula. This problem involves statistics and probability theory applied to real-world data from Statistics Canada.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation