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If a is a number that is randomly selected from Set A, and b

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If a is a number that is randomly selected from Set A, and b [#permalink]

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New post 06 Feb 2014, 05:57
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Question Stats:

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A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

OE
[Reveal] Spoiler:
Probability = (Desired outcomes / Possible outcomes)

Possible outcomes:
5 integers in Set A & 4 in Set B. An integer in Set A may be paired with each integer in Set B for total of 4 pairs. However, 5 integers in Set A → Overall 5 x 4 possible outcomes for ab.

Find how many positive & negative pairs are possible.
Set A contains 2 positive integers (1, 6), & Set B contains 2 positive integers (2, 7).
Together, they form 2 x 2 = 4 pairs.
Likewise, Set A contains 2 negative integers (-3, -8), & Set B contains 2 negative integers (-1, -4).
Together, they form 2 x 2 = 4 pairs.
0, member of Set A, is neither positive nor negative, and its product with any number will always result in 0.

Question stem specifies that ab must be positive and greater than 0, so do not need to consider pairs that contain 0 when finding desirable outcomes.

(Desired outcomes / Possible outcomes) = (4 + 4) / 20 = 8 / 20 = 2/5


Hi, I want to know whether OE is the fastest way to solve this question, please.
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Feb 2014, 04:45, edited 1 time in total.
Edited the question.

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Re: If a is a number that is randomly selected from Set A, and b [#permalink]

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New post 06 Feb 2014, 08:22
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goodyear2013 wrote:
A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
1/4
1/3
2/5
4/9
1/2

OE
[Reveal] Spoiler:
Probability = (Desired outcomes / Possible outcomes)

Possible outcomes:
5 integers in Set A & 4 in Set B. An integer in Set A may be paired with each integer in Set B for total of 4 pairs. However, 5 integers in Set A → Overall 5 x 4 possible outcomes for ab.

Find how many positive & negative pairs are possible.
Set A contains 2 positive integers (1, 6), & Set B contains 2 positive integers (2, 7).
Together, they form 2 x 2 = 4 pairs.
Likewise, Set A contains 2 negative integers (-3, -8), & Set B contains 2 negative integers (-1, -4).
Together, they form 2 x 2 = 4 pairs.
0, member of Set A, is neither positive nor negative, and its product with any number will always result in 0.

Question stem specifies that ab must be positive and greater than 0, so do not need to consider pairs that contain 0 when finding desirable outcomes.

(Desired outcomes / Possible outcomes) = (4 + 4) / 20 = 8 / 20 = 2/5


Hi, I want to know whether OE is the fastest way to solve this question, please.

I am happy to help with that !! First you should pick one scenario in which you can get a positive number so let's say you pick "1" from Set A and "2" from Set B so probability of picking "1" is 1/5 and probability of picking "4" from Set B is 1/4 , count how many times this scenario can happen you will find that it is 8 times !! so 8*(1/5*1/4)= 8/20=2/5 !!! Hope it was clear :)

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Re: If a is a number that is randomly selected from Set A, and b [#permalink]

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New post 07 Feb 2014, 04:47
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goodyear2013 wrote:
A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

OE
[Reveal] Spoiler:
Probability = (Desired outcomes / Possible outcomes)

Possible outcomes:
5 integers in Set A & 4 in Set B. An integer in Set A may be paired with each integer in Set B for total of 4 pairs. However, 5 integers in Set A → Overall 5 x 4 possible outcomes for ab.

Find how many positive & negative pairs are possible.
Set A contains 2 positive integers (1, 6), & Set B contains 2 positive integers (2, 7).
Together, they form 2 x 2 = 4 pairs.
Likewise, Set A contains 2 negative integers (-3, -8), & Set B contains 2 negative integers (-1, -4).
Together, they form 2 x 2 = 4 pairs.
0, member of Set A, is neither positive nor negative, and its product with any number will always result in 0.

Question stem specifies that ab must be positive and greater than 0, so do not need to consider pairs that contain 0 when finding desirable outcomes.

(Desired outcomes / Possible outcomes) = (4 + 4) / 20 = 8 / 20 = 2/5


Hi, I want to know whether OE is the fastest way to solve this question, please.


For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:

P(positive, positive) = 2/5*2/4 = 4/20;
P(negative, negative) = 2/5*2/4 = 4/20.

P = 4/20 + 4/20 = 8/20 = 2/5.

Answer: C.

Hope it's clear.
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Re: If a is a number that is randomly selected from Set A, and b [#permalink]

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New post 07 Feb 2014, 11:16
Pick both +ve: 2/5 * 2/4 =1/5.
Pick both -ve: 2/5 * 2/4 = 1/5.
Required prob = 1/5 + 1/5 = 2/5.

Remember: "0" is neither +ve nor -ve.

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Re: If a is a number that is randomly selected from Set A, and b [#permalink]

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New post 18 Jan 2016, 12:03
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HI All,

As far as probability questions are concerned, this one is fairly straight-forward. Even if you're not perfectly knowledgeable about all of the variations that probability questions can take and/or you might not be comfortable with all of the math 'steps' involved, you can still answer this question with a bit of 'brute force'...

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

Since Set A has 5 terms and Set B has 4 terms, there are (5)(4) different 'pairs' of numbers that can be selected. We're asked for the probability that the product of that pair is POSITIVE. We can simply list out the possible pairs that fit this restriction:

1 and 2
1 and 7
-3 and -1
-3 and -4
6 and 2
6 and 7
-8 and -1
-8 and -4

There are 8 pairs (out of 20 possible) that fit what we're looking for. 8/20 = 2/5

Final Answer:
[Reveal] Spoiler:
C


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Re: If a is a number that is randomly selected from Set A, and b [#permalink]

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New post 26 Sep 2017, 02:58
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Re: If a is a number that is randomly selected from Set A, and b   [#permalink] 26 Sep 2017, 02:58
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