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1000 used car tires are being evaluated by a major insurance company. The quality of the...

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Basic Math

  1. 1000 used car tires are being evaluated by a major insurancecompany. The quality of the tiers are based on the depth of thetreads and years in use. The results from 1000 tires are summarizedas 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 (lessthan 2 years old), and let B denote the tire haslow depth for treads (less than 3 mm). Determine the number ofcastings 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 notnew with high treads depth?
  5. What is the probability that a randomly selected tire is notnew with low treads depth?
  6. If a selected tire was found to be new, find the probabilitythat it is with high treads depth.
  7. Find P(A | B)

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