Question

1. 1000 used car tires are being evaluated by a major insurance company. The quality of the tiers are based on the depth of the treads and years in use. The results from 1000 tires are summarized as the following:

		Years in use
		Less than 2 yrs	More than 2years
Treads depth	> 3mm	700	150
	< 3mm	50	100

Let A denote the event that a tire is new (less than 2 years old), and let B denote the tire has low depth for treads (less than 3 mm). Determine the number of castings in

1. Put in writing what A∩ B means.
2. Find A∩ B
3. Find A∪ B¢
4. What is the probability that a randomly selected tire is not new with high treads depth?
5. What is the probability that a randomly selected tire is not new with low treads depth?
6. If a selected tire was found to be new, find the probability that it is with high treads depth.
7. Find P(A | B)

Answer 1