Question

car inspections are due yearly. twenty percent of all cars that undergo the annual state inspection will fail the inspection. assume that the cars independently undergo the yearly inspection. the expected number of cars inspected before a car fails inspection is:

Answer 1

The expected number of car inspections before encountering a failed inspection, with a failure rate of 20%, is calculated to be 5 using the geometric distribution's expected value formula.

Step-by-step explanation:

The subject of the question involves calculating the expected number of car inspections before a car fails, given a 20% failure rate. This is a probability question that can be solved using the concept of geometric distribution. The expected value (E) for a geometrically distributed random variable is given by the formula E = 1/p, where p is the probability of success (in this case, the probability of a car failing the inspection).

Here, we are given that p = 0.20 (20%). So, the expected number of car inspections before one fails is E = 1/0.20 = 5. Therefore, on average, one would expect 5 cars to be inspected before encountering a failure.