(2)Acertain sports car comes equipped with either an automatic or a manual trans
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Question
(2)Acertain 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 .10 07 Transmission Tvpe Black Red 15 18 = (automatic transmission), B = {black), and C = { white} Suppose you randomly select a car, then calculate the probabilities of the following events. a. b. c. d. e. the color of the car is "black" the color of the car is not white the color of the car is either "white" or "black" the car is "automatic" and the color of the car is "black" the car is "automatic" or the color of the car is "black"Explanation / Answer
a. P [the colour of the car is black] = 0.11+0.15 = 0.26
b. P [ the colour of the car is white ] = 0.13+0.15 = 0.28
P [ the colour of the car is not white ] = 1-0.28 = 0.72
c. P [the colour of the car is either white or black] = P [ colour of the car is white ] + P [ colour of the car is black ]
= 0.28 + 0.26 = 0.54
d. P [ the car is autometic and the colour is black ]
= 0.11
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