An automotive repair shop sells three kinds of tires: budget (25% of sales), standard (65% of sales), and commercial (10% of sales). The probability that a tire must be replaced in its first year of use differs for each type of tire, given in the following table. Type of Tire Probability that the a tire of this type must be replaced in its first year of use Budget 0.20 Standard 0.10 Commercial 0.01 One tire is chosen randomly. Define the following events: B: The chosen tire is a budget tire R: The chosen tire will need to be replaced in its first year of use Compute the following probabilities: (a) P(R) (b) P(B | R) (c) P(R | B') (d) P(B | R') [HINT: For events E1 and E2, P(E1' | E2) = 1 - P(E1 | E2)]