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# A car dealer has a large inventory of cars of which 25 percent are red

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Intern
Joined: 26 Apr 2018
Posts: 39
A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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30 Jul 2018, 05:43
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00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:56) correct 26% (01:58) wrong based on 115 sessions

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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

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Joined: 02 Sep 2009
Posts: 51218
Re: A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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30 Jul 2018, 06:15
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1
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

25 percent are red;
15 percent are blue;
30 percent are black;
30 percent are other colors.

For each color of car, 70 percent are equipped with automatic transmission and of these, 20 percent have air-conditioning, so 0.7*0.2 = 0.14 of all the cars have BOTH automatic transmission and air-conditioning.

P(not black + both automatic transmission and air-conditioning) = P(red, blue or other colors but black)*P(BOTH automatic transmission and air-conditioning) = (25 + 15 + 30)/100*0.14 = 0.098.

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Posts: 135
A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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30 Jul 2018, 07:54
Strange and non-efficient approachtime : ))

Assume that there are 100 cars
25 Red
15 Blue
30 Black
30 Other

70% of each color is with AT and from them 20% is with AC
Red - 25*$$\frac{70}{100}$$*$$\frac{20}{100}$$=$$\frac{7}{2}$$ cars
Blue - 15*$$\frac{70}{100}$$*$$\frac{20}{100}$$=$$\frac{21}{10}$$ cars
Other - 30*$$\frac{70}{100}$$*$$\frac{20}{100}$$=$$\frac{21}{5}$$

Total cars (except Black) with AT and AC - $$\frac{7}{2}$$+$$\frac{21}{10}$$+$$\frac{21}{5}$$=9.8

Probability not to choose Black $$\frac{70}{100}$$ (except black we have 70 cars) and from the chosen not black to choose a car with AT and AC $$\frac{9.8}{70}$$
As and means multiplication in probability we have got $$\frac{70}{100}$$*$$\frac{9.8}{70}$$=0.098 cars which means 9.8% from initial 100 cars

IMO
Ans: A

Yuhuu. P.S if you dont wont to deal with confusing numbers, read Bunuel's post above, have a nice day
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A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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30 Jul 2018, 13:11
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 rule
The 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 rule
70 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

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Re: A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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01 Aug 2018, 15:28
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%

We can assume there are a total of 1000 cars. Thus, 0.7 x 1000 = 700 of them are equipped with automatic transmission and 0.2 x 700 = 140 of these cars have air-conditioning. Since 30% of the 140 cars are black, then 0.3 x 140 = 42 cars are black. So 140 - 42 = 98 non-black cars have both an automatic transmission and air-conditioning. Therefore, the probability is 98/1000 = 9.8/100 = 9.8%.

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Intern
Joined: 03 Feb 2016
Posts: 13
Location: China
Re: A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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04 Aug 2018, 06:17
this is how i solved it:

.25x = R
.15x = B
.30x = BL
.30x = O

Probability of picking not black and with Automatic trans and AC =( (.30x+.15x+.25x )*.70*.20)/Total probability

9.8/1 = 9.8

Senior Manager
Joined: 22 Feb 2018
Posts: 411
A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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12 Sep 2018, 07:43
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

OA: A
Let the total number of car $$= 1000$$
Number of Black colored car $$= \frac{30}{100}*1000 = 300$$
Number of Not Black colored car $$= 1000 -300 = 700$$
Number of Not Black colored car with automatic transmission$$= \frac{70}{100}*700 = 490$$
Number of Not Black colored car with automatic transmission and air conditioning $$= \frac{20}{100}*490= 98$$
probability that a car chosen at random will not be black and will have both automatic transmission and air-conditioning$$= \frac{98}{1000}*100 = 9.8$$%
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Re: A car dealer has a large inventory of cars of which 25 percent are red  [#permalink]

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12 Sep 2018, 08:20
Quick elimination tip

When you have multiple probabilities less than 1 that you multiple together, the results will be LESS than the smallest probability. So, for instance, 5% of 20% is LESS than 5%. No duh, right? Here the probabilities are 70%, 70%, and 20%. So, the right answer is less than 20%. Eliminate c, d, and e.

What feels correct now? Is 70 percent of 70 percent of 20 percent around 15 or around 10? Well, 75% of 20 is 15....

Think before you math.
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http://www.indigoprep.com

Re: A car dealer has a large inventory of cars of which 25 percent are red &nbs [#permalink] 12 Sep 2018, 08:20
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