Question

It is estimated that only 68% of drivers wear their safety belt.

Part A: What is the probability that exactly 3 drivers are wearing their safety belts if a police officer pulls over five drivers? (5 points)

Part B: What is the probability the next driver wearing their safety belt that the police officer pulls over is the fifth driver? (5 points)

Answer 1

Explanation:

we have 2 probabilities :

1. that a driver is wearing their safety belts : 0.68

2. that the driver is NOT wearing the safety belts :

1-0.68 = 0.32

A.

3 drivers are wearing it, 2 are not is a combination of

0.68³×0.32²

and how many combinations of these 5 probabilities can we have (e.g. the first 3 are wearing them, or the last 3 are wearing them, or ...) ?

that is 5 over 3 combinations :

5! / (3! × (5-3)!) = 5! / (3! × 2!) = 5×4/2 = 5×2 = 10

so, we have

10×0.68³×0.32² = 0.321978368

B

I am not sure I understand the question.

I assume this means from the 5 drivers they pull over the first 4 don't wear the seat belts, and only the fifth does.

so that is then

0.32⁴×0.68

and only one combination is possible. so, the result is just the product of these probabilities :

0.32⁴×0.68 = 0.0071303168