A certain sports car comes equipped with either an automatic or a manual transmi

Question

A certain sports car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. Relevant probabilities for various combinations of transmission type and color are given in the accompanying table Color White 13 .15 Blue Black 10 07 Transmission Type Red 15 .18 Let A = (automatic transmission), B = {black), and C = (white). Suppose you randomly select a car, then calculate the probabilities of the following events a. the color of the car is "black" b. the color of the car is not white c. the color of the car is either "white" or "black d. the car is "automatic" and the color of the car is "black e. the car is "automatic" or the color of the car is "black"

Explanation / Answer

Here' answer to the question :
a. P(Black) = .11+.15 = .26

b. P(not white) = 1-P(white) = 1-.13-.15 = .72

c. P(white or black) = .11+.15+.13+.15 = .54

d. P(automatic and black) = .11

e. P(automatic or black) = .13+.10+.11+.11+.15+.11-.11 = 0.60

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