This is a stats problem.

Twenty percent of all trucks undergoing a certain inspection will fail the inspection. Assume that trucks are independently undergoing this inspection, one at a time. The expected number of trucks inspected before a truck fails inspection is...?

I belive this is a geometric probability problem, but I don't know how to solve it. Please help.

This is a geometric probability problem. (Chapter 5)

P = 0.20
E(X) = 1/p = 1/0.2 = 5 trucks

Yes, you are correct. This problem can be solved using geometric probability.

In a geometric probability problem, we are interested in the number of trials required before a certain event occurs.

In this case, the event is a truck failing inspection, and the probability of this event occurring is 20% or 0.20.

The expected number of trucks inspected before a truck fails inspection can be calculated using the formula for the expected value of a geometric random variable: E(X) = 1/p.

Here, p is the probability of the event occurring, which is 0.20.

So, the expected number of trucks inspected before a truck fails inspection is:

E(X) = 1/0.20 = 5

Therefore, the expected number of trucks inspected before a truck fails inspection is 5.

Yes, you're correct, this is a geometric probability problem. In order to find the expected number of trucks inspected before a truck fails the inspection, we need to find the expected value of a geometric random variable.

In a geometric distribution, we're interested in the number of trials needed to achieve the first success. In this case, a "success" refers to a truck passing the inspection.

The geometric probability formula is given by:
P(X = k) = (1 - p)^(k-1) * p

Where:
- X is the number of trials until the first success,
- p is the probability of success on any given trial (in this case, the probability of a truck failing the inspection),
- k is the number of trials until the first success.

In this problem, p = 0.20 (since 20% of the trucks fail the inspection).

To find the expected value (mean) of the geometric distribution, we can use the formula:
E(X) = 1/p

Substituting p = 0.20 into the formula, we get:
E(X) = 1/0.20 = 5

Therefore, the expected number of trucks inspected before a truck fails the inspection is 5.

To solve these types of problems, you'll need to have a strong understanding of probability and the geometric distribution. You can calculate the expected value using the formula provided, but make sure you have the correct values for p and k.