how many tries are expected to reach success if success has a 5% chance

The expected number of tries to reach a success when the probability of success on each try is 5% can be found using the formula for the **expected number of trials** in a geometric distribution:

\[
E(X) = \frac{1}{p}
\]

Where:
- \( E(X) \) is the expected number of trials,
- \( p \) is the probability of success on each trial.

Here, \( p = 0.05 \) (5% chance of success). Substituting this into the formula:

\[
E(X) = \frac{1}{0.05} = 20
\]

So, **20 tries** are expected to reach the first success.

Would you like more details or have any questions?

### Related Questions:
1. What is the variance of the number of trials in a geometric distribution?
2. How does the expected number of tries change if the probability of success is 10%?
3. What is the probability of succeeding within 10 tries if the chance of success is 5%?
4. How does the expected value change in a binomial distribution compared to a geometric distribution?
5. How can we model repeated successes with a 5% chance instead of just the first success?

**Tip:** The geometric distribution models the number of trials until the first success in independent trials.

Calculate the expected number of tries needed to reach a success when the probability of success is 5%. Learn how to use the geometric distribution formula to solve this problem, suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation