bettatantalo wrote:
A car dealer has a large inventory of cars of which 25 percent are red, 15 percent are blue, 30 percent are black and the remainder are other colors. For each color of car, 70 percent are equipped with automatic transmission and of these, 20 percent have air-conditioning. What is the probability that a car chosen at random will not be black and will have both automatic transmission and air-conditioning?
(A) 9.8%
(B) 14%
(C) 30%
(D) 70%
(E) 90.2%
Question from MBA Center GMAT study book
Probability - Use the complement rule and the AND rule
Complement rule: P(not A) = 1 - P(A)
AND rule: If A and B are independent events, then
P(A and B) = P(A) * P(B)
Complement ruleThe car will be either black or some other color that is NOT black.
P(Black) + P(not Black) = 1
P(not Black) = 1 - P(black)
P(not Black) = (1 - .30) = .70
The AND rule70 percent of all cars (70% of "each color of car") have automatic transmissions ("AT")
Of that 70 percent, 20 percent have air conditioning, "AC"
AT and AC are independent events; the occurrence of one does not change the probability of the occurrence of the other
For all cars, P(AT and AC) = P(AT) * P(AC)
(0.7) * (0.2) = 0.14
Probability of
not black AND
both automatic transmission and air-conditioning?
P(not Black) is also an independent event
P(not Black and AT and AC) =
P(not Black) * P(AT and AC) =
(0.7) * (0.14) = .098 = 9.8 percent
Answer A
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