Question

Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use.

what is the probability that the first unbelted driver is in the 6th car stopped?

Answer 1

20%

Explanation:

The probability that the first unbelted driver is in the 6th car stopped is
(1 - 0.20)^5 * 0.20,
where 0.20 is the probability that a driver does not wear their seatbelt (20%),
and (1 - 0.20)^5 is the probability that the first 5 cars stopped all have drivers who wear their seatbelts.

This simplifies to (0.8)^5 * 0.2 = 0.32768 * 0.2 = 0.065536.