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Probability of selecting a car with both A and Power window

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Probability of selecting a car with both A and Power window [#permalink] New post   18 Sep 2019, 13:40
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In a lot of CMW cars, \(\frac{1}{4}\) of the cars have AC and \(\frac{3}{5}\) of the cars have power windows.

Quantity A
Quantity B
Probability of selecting a car with both AC and Power window
\(\frac{2}{9}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: Probability of selecting a car with both A and Power window [#permalink] New post   20 Sep 2019, 05:40
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Carcass wrote:
In a lot of CMW cars, \(\frac{1}{4}\) of the cars have AC and \(\frac{3}{5}\) of the cars have power windows.

Quantity A
Quantity B
Probability of selecting a car with both A and Power window
\(\frac{2}{9}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


OA is not provided

KEY CONCEPT: It could be the case that there are no cars with BOTH AC and Power Windows, or it could be the case that some cars have BOTH AC and Power Windows.

Let's examine two possible cases
case i: There are 20 cars. 5 have BOTH features, 7 have power windows only, and 8 have neither feature.
We get:
Quantity A: 5/20 = 1/4
Quantity B: 2/9
In this case, Quantity A is greater

case ii: There are 20 cars. 5 have AC only, 12 have power windows only, and 3 have neither feature.
We get:
Quantity A: 0/20
Quantity B: 2/9
In this case, Quantity B is greater

Answer: D

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Re: Probability of selecting a car with both A and Power window [#permalink] New post   19 Sep 2019, 01:16
Is the answer B?

Considering P(AC and Power window) = (1/4) * (3/5) = 3/20

and 3/20 < 2/9 so B

or is it D, since it is not mentioned whether the events are independent or mutually exclusive?
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Re: Probability of selecting a car with both A and Power window [#permalink] New post   16 Nov 2022, 09:14
I did a double matrix and moved around the elements a bit so I could see a MAX of AC and Power Windows, and then a Minimum. Turns out (if my calculations are correct), that there can actually be 0 between the two of them.
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Re: Probability of selecting a car with both A and Power window [#permalink] New post   21 Nov 2022, 05:54
Didn't understand this properly can anyone explain clearly.
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Re: Probability of selecting a car with both A and Power window [#permalink] New post   21 Nov 2022, 10:24
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Here with a bit of logic we can have the solution

1/4 ONLY AC

3/5 ONLY PW

So, 3/4 have NO AC

2/5 have NO PW

But the overlap area between 1/4 ONLY AC and 3/4 NO AC is variable

1/4< P < 3/4 Therefore we can have a number P smaller than 2/9 or greater than 2/9

D is the answer
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Re: Probability of selecting a car with both A and Power window [#permalink] New post   06 Apr 2023, 23:18
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I think the maximum probability of having both features is 1/4 i.e. probability of having AC ( this is the case where all ac cars have power window). The minimum probability is 0 ( no ac car has power window). So, we have 2 cases, 1 bigger and 1 smaller than 2/9. Answer should be D.

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Re: Probability of selecting a car with both A and Power window [#permalink] New post   19 May 2024, 01:34
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Re: Probability of selecting a car with both A and Power window [#permalink]
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