2. A certain new limited-edition sports car comes equipped with either an automa

Question

2. A certain new limited-edition sports car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. The number of cars manufactured with various combinations of transmission type and color are given in the table below. Let E = automatic transmission), F {black), and G-(white). (a) Calculate P(E), P(F), P(EnF). (b) Calculate both P(EF) and P(FE) and explain in context what each of these probabilities represents. (c) Calculate and interpret P(EG) and P(EG) Automatic Manual White 15 15 Blue 10 Black 10 15 Red 10 30

Explanation / Answer

Answer to the following question :

E = auto transmission
F = {black}
G = {white}

a. P(E) = (15+10+10+10)/(15+10+10+10+15+5+15+30) = .41
P(F) = (10+15)/(15+10+10+10+15+5+15+30) = .23
P(E and F) = (10/(15+10+10+10+15+5+15+30) = .091

b. P(E|F) = 10/10+15 = 2/5
P(F|E) = 10/(15+10+10+10) = .22

c. P(E|G) = 15/15+15 = 1/2
P(E|Gc) = (10+10+10) / (10+10+10+5+15+30) = .375

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