Question

Let X be a binomial random variable with number of trials 100 and expected value 20. What is the probability of success of X?

Answer 1

In a binomial distribution, the expected value \( E(X) \) is given by the formula:

\[
E(X) = n \cdot p
\]

where \( n \) is the number of trials, and \( p \) is the probability of success.

In this case, we are given:
- The number of trials, \( n = 100 \)
- The expected value, \( E(X) = 20 \)

We can use the formula for expected value to find \( p \):

\[
20 = 100 \cdot p
\]

To isolate \( p \), we solve for \( p \):

\[
p = \frac{20}{100} = 0.2
\]

Therefore, the probability of success \( p \) is \( \boxed{0.2} \).