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Two integers will be randomly selected from the sets above,

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Joined: 02 Dec 2012
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Two integers will be randomly selected from the sets above,  [#permalink]

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02 Dec 2012, 06:51
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Difficulty:

15% (low)

Question Stats:

79% (01:28) correct 21% (01:46) wrong based on 1052 sessions

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A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33
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Joined: 02 Sep 2009
Posts: 52348
Re: Two integers will be randomly selected from the sets above,  [#permalink]

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02 Dec 2012, 06:52
1
8
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

The total number of pairs possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.

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Joined: 18 Feb 2012
Posts: 11
Re: Two integers will be randomly selected from the sets above,  [#permalink]

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02 Dec 2012, 17:51
7

I pick a number from Set A. No matter which number I pick, my chance of chosing the right number (which gives A+B = 9) in Set B will be 1/5.

Therefore 1/5 = 0.20 => B
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Manager
Joined: 07 Apr 2014
Posts: 111
Re: Two integers will be randomly selected from the sets above,  [#permalink]

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11 Sep 2014, 00:54
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

total possibility -- 4c1 *5c1

possible stuff: (2,7), (3,6), (4,5),(5,4)= 4

4/20= 1/5= 0.2
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Joined: 23 Mar 2016
Posts: 29
Schools: Tulane '18 (M\$)
Re: Two integers will be randomly selected from the sets above,  [#permalink]

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02 May 2016, 14:23
Probability of A (any number) AND B(4 of 5).
We don't need to calculate each and every probability, rather the overall. But let's go the long way to see the theory behind the easy way.

A = { 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

If we choose 2 from A, the only way we can get a sum of 9 is if we choose 7 from B.

2 from A = .25 probability of occurring (1/4)
7 from B = .20 probability of occurring (1/5)
(1/4)*(1/5) = 1/20
If you do this for each number in A, you get the same outcome, 1/20
add all of these up, and you get 1/20 + 1/20 + 1/20 + 1/20 = 4/20 = 4/20(5) = 20/100 = .2 to get the sum of 9 when choosing a number from A and its corresponding "match" from B (3+5)(2+7)(4+5)(5+4)

Now to take the easy route.
For any number in A, you have a 4/4 chance of picking a number (100% strike rate)
For any number in B, you have a 4/5 chance of picking a number (80% strike rate)
4/4 * 4/5 = 16/20 chance of getting any addition answer, therefore a 4/20 chance of getting 9 as a sum = 20%, .2
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Re: Two integers will be randomly selected from the sets above,  [#permalink]

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03 May 2016, 04:46
2
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

Solution:

To determine the probability that the sum of the two integers will equal 9, we must first recognize that probability = (favorable outcomes)/(total outcomes).

Let’s first determine the total number of outcomes. We have 4 numbers in set A, and 5 in set B, and since we are selecting 1 number from each set, the total number of outcomes is 4 x 5 = 20.

For our favorable outcomes, we need to determine the number of ways we can get a number from set A and a number from set B to sum to 9. We are selecting from the following two sets:

A = {2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

We will denote the first number as from set A and the second from set B. Here are the pairings that yield a sum of 9:

2,7
3,6
4,5
5,4

We see that there are 4 favorable outcomes. Thus, our probability is 4/20 = 0.25, Answer C.
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Re: Two integers will be randomly selected from the sets above,  [#permalink]

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22 Feb 2018, 13:04
Hi All,

Probability questions are based on the probability formula:

(Number of ways that you "want") / (Total number of ways possible)

Since it's usually easier to calculate the total number of possibilities, I'll do that first. There are 4 options for set A and 5 options for set B; since we're choosing one option from each, the total possibilities = 4 x 5 = 20

Now, to figure out the number of duos that sum to 9:

2 and 7
3 and 6
4 and 5
5 and 4

4 options that give us what we "want"

4/20 = 1/5 = 20% = .2

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Joined: 12 Sep 2017
Posts: 28
Re: Two integers will be randomly selected from the sets above,  [#permalink]

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10 Apr 2018, 05:45
Bunuel wrote:
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

The total number of pairs possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.

Hi Bunuel

Is {4,5} and {5,4} not same?
Math Expert
Joined: 02 Sep 2009
Posts: 52348
Re: Two integers will be randomly selected from the sets above,  [#permalink]

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10 Apr 2018, 05:51
@s wrote:
Bunuel wrote:
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

The total number of pairs possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.

Hi Bunuel

Is {4,5} and {5,4} not same?

(4, 5) is 4 from A and 5 from B.

(5, 4) is 5 from A and 4 from B.

Those are two different cases.
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Re: Two integers will be randomly selected from the sets above, &nbs [#permalink] 10 Apr 2018, 05:51
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