3. A certain sports car comes equipped with either an auto four colors. Relevant

Question

3. A certain sports car comes equipped with either an auto four colors. Relevant probabilities for various combinations of transmission type and color were calculat production records, and are given in the accompanying table. matic or manual transmission, and the car is available in one of ed from Transmission Type Red 13 15 10 07 18 white, G-gold. B black and R-red . R6) rayetA-automatic, M-manual, w B) from the table. a. Calculate P(A), P(B), and identify PIA a sentence to explain in context what each of these probabilities to b. Calculate botht 5) and P(B)A), and use represents. df given P cniG) - r C

Explanation / Answer

Answer to the following is below:

a.

P(A) = .13+.10+.11+.11 = .45

P(B) = .11+.15 = .26

P(A and B) = .11

b. P(A|B) = P(A and B)/P(B) = .11/.11+.15 = 11/26

So, this is : Given it is a Black Color car, the chances that is a transmission Automatic is 11/26

P(B|A) = P(A and B) /P(A) = .11/.45 = 11/45

So, this is : Given it is a Automatic car, the chances that is a Black Automatic is 11/45

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