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Two integers will be randomly selected from the sets above, one

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carcass
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Two integers will be randomly selected from the sets above, one [#permalink] New post   Updated on: 06 Sep 2022, 00:59
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A = {3, 4, 5, 6}
B = {3, 4, 5, 6, 7}

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 10?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.40


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B

Originally posted by carcass on 05 Sep 2022, 23:40.
Last edited by Bunuel on 06 Sep 2022, 00:59, edited 1 time in total.
Renamed the topic.
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Re: Two integers will be randomly selected from the sets above, one [#permalink] New post   06 Sep 2022, 00:13
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ways to select an integer from A ; 4c1 and from B 5c1
total ways to select two integers 4*5 ;20
possible pairs of integers whose sum is 10
(3,7) ; ( 4,6) ; ( 5,5) ; ( 6,4)
4/20 ; 0.2
option B

carcass wrote:
A = {3, 4, 5, 6}
B = {3, 4, 5, 6, 7}

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 10?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.40


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Re: Two integers will be randomly selected from the sets above, one [#permalink] New post   06 Sep 2022, 00:59
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A = {3, 4, 5, 6}
B = {3, 4, 5, 6, 7}

Each number in A has a single matching number in B that when summed will give 10.
All of these numbers have a single correlating integer in which together sum to 10.

Probability that the sum of the two integers drawn will equal 10: \(\frac{4}{4}*1/5\)

\(= \frac{1}{5}\) or \(20\)%

Answer B
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Re: Two integers will be randomly selected from the sets above, one [#permalink] New post   06 Sep 2022, 01:01
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carcass wrote:
A = {3, 4, 5, 6}
B = {3, 4, 5, 6, 7}

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 10?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.40


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Re: Two integers will be randomly selected from the sets above, one [#permalink] New post   06 Sep 2022, 02:08
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For this question, thinking of probability as probability = \(\frac{no. of desired outcomes}{no. of total outcomes}\) might be easier

No. of total outcomes = \(4*5 = 20\)

For desired outcomes:
A+B
2+7
3+6
4+5
5+4
There's only 4 possible ways

So \(probability = \frac{4}{20} = \frac{1}{5} = 0.2\)
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Re: Two integers will be randomly selected from the sets above, one [#permalink] New post   06 Sep 2022, 22:11
carcass wrote:
A = {3, 4, 5, 6}
B = {3, 4, 5, 6, 7}

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 10?

(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.40



Total outcomes = \(4c1 * 5c1 = 4*5 = 20\) (Picking 1 from 4 options from the first set and Picking 1 from 5 options from the second set)

Favorable outcomes (Sum = 10): There are two ways to go about this, either choose 1 from the first set and the corresponding from the other set which summed together equals 10 or the other way around. Both ways will get you the following

(3,7), (4,6), (5,5), and (6,4) = 4 favorable outcomes

Probability = \(\frac{4}{20} = 0.20\)

Answer - B
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Re: Two integers will be randomly selected from the sets above, one [#permalink]
06 Sep 2022, 22:11
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