4 An automotive repair shop sells three kinds of tires budge

4) An automotive repair shop sells three kinds of tires: budget (20% of sales, standard (30% of sales, and commercial (50% 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 Probability that the a tire of this type must be Tire replaced in its first year of use Budget 0.15 Standard 0.10 0.05 Commercial One tire is chosen randomly. Define the following events: S: The chosen tire is a standard tire R: The chosen tire will need to be replaced in its first year of use Compute the following probabilities: (a) POR) (b) PSIR) (c) POS\' IR\') HINT: For two events El and E2, POE\' E 2) 1 -P(Ei l E2)]

Solution

a)

P(R)= 0.15+0.10+0.05 = 0.3

b)

P(S/R) = 0.10

c)

P(S´ / R´) = 1- 0.10 = 0.90