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At a certain car dealership, the 40 vehicles equipped with

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At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 13 Jul 2011, 08:08
1
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A
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Difficulty:

  25% (medium)

Question Stats:

57% (02:04) correct 43% (02:32) wrong based on 65 sessions

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At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

A. 41/50
B. 9/50
C. 6/50
D. 21/25
E. 8/25

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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 29 Nov 2017, 09:46
AnkitK wrote:
At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?


We are given that the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. We can let n = the total number of cars and create the following equation:

40 = 0.8n

n = 40/0.8 = 50

Thus, there are a total of 50 cars at the dealership. Furthermore, we are given that there are 15 convertibles, and 14 of them are equipped with air conditioning.

So, the the probability that a randomly selected vehicle will be a convertible or a car with air conditioning is:

[(15 + 40) - 14]/50 = 41/50

Note that we double-counted the 14 cars that are both convertibles and are cars with air conditioning, and so we had to subtract the 14 from the total.
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 13 Jul 2011, 08:43
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AnkitK wrote:
At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

ConvertibleNon-ConvertibleTotal
AC142640
Non-AC1910
Total153550


Fill it in this order:

AC cars=40
Total Cars=40/0.8=50
Non-AC Cars=50-40=10
Total Convertibles=15
Convertible AC=14
Convertible Non-AC=15-14=1
Non-Convertible/Non-AC=10-1=9
Non-Convertible/AC=40-14=26

Total Convertible+All AC= 15+26=41
Total cars=50

P=41/50.

Ans: 41/50
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 23 Jul 2011, 23:18
gaurav1083 wrote:
fluke wrote:
AnkitK wrote:
At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

ConvertibleNon-ConvertibleTotal
AC142640
Non-AC1910
Total153550


Fill it in this order:

AC cars=40
Total Cars=40/0.8=50
Non-AC Cars=50-40=10
Total Convertibles=15
Convertible AC=14
Convertible Non-AC=15-14=1
Non-Convertible/Non-AC=10-1=9
Non-Convertible/AC=40-14=26

Total Convertible+All AC= 15+26=41
Total cars=50

P=41/50.

Ans: 41/50


+1 for 41/50.
Used same approach.


Fluke, we din't count 14 while calculating all AC..is it because it was already counted while calculating Convertible?? hence, re-count would contribute to a double figure??

Pls correct me, if I am wrong..
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 21 Oct 2013, 22:45
Till the table finding, it seems all correct as per my findings. But, since the question is asking either A.C or Convertible ...not both.
so, my answer is coming as below.
1 (Non A.C and Convertible) + 26 (A.C and non-convertible) = 27.
Therefore, require probability = 27/50. Please correct me if seems wrong.
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 24 Jan 2014, 02:52
1
total cars is 50. since 40 is 80% of 50.

40 cars are AC---given.
15 cars are convertible of which 14 are AC. means
14 are AC+convertible.
1 is Non-AC convertible.
AC+non-convertible is 40 -14 = 26.
9 are neither.

So either AC or convertible = 26+14+1 = 41.

Probability is 41/50.
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 24 Jan 2014, 07:32
Is this really a "700+ difficulty" question?
It was easy to solve (or to write down all that stuff) though it took me 2min 27sec.
Should be a Verbal question with all that writing :D :D
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 31 Jan 2014, 17:15
other way to see it is:

9 cars are neither AC nor Convertibles:

So 50-9=41 (either AC or Convertibles)

Hence prob: 41/50
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Re: At a certain car dealership, the 40 vehicles equipped with  [#permalink]

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New post 27 Nov 2017, 05:43
1
AnkitK wrote:
At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

Spoiler: :: OA
OA:41/50



hi

80% = 40
so, 100% = 50 = total

now, 50 = 40 + 15 - 14 + none
so, niether A/C nor convertible = 9

probability:

(either convertible or equipped with A/C) / total

= (50 - 9) / 50
= 41/50

thanks
:cool:
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Re: At a certain car dealership, the 40 vehicles equipped with &nbs [#permalink] 27 Nov 2017, 05:43
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