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If two different numbers are randomly selected from set { 1,

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rxs0005
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If two different numbers are randomly selected from set { 1, [#permalink] New post   Updated on: 30 Aug 2023, 02:36
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If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)

B. \(\frac{7}{10}\)

C. \(\frac{4}{5}\)

D. \(\frac{9}{10}\)

E. \(\frac{19}{20}\)

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C

Originally posted by rxs0005 on 23 Jul 2010, 08:52.
Last edited by Bunuel on 30 Aug 2023, 02:36, edited 3 times in total.
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Re: If two different numbers are randomly selected from set { 1, [#permalink] New post   23 Jul 2010, 13:06
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If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)


Let's determine the probability of the opposite event first and then subtract that value from 1. The opposite event occurs when we select two different numbers such that their sum is less than or equal to 4.

The total number of outcomes is \(C^2_5=10\), which represents choosing 2 different numbers from a set of 5.

The outcomes where the \(sum \leq 4\) are only (1,2) and (1,3), totaling 2 outcomes.

Thus, \(P = 1 - \frac{2}{10} = \frac{4}{5}\).


Answer: C
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Re: If two different numbers are randomly selected from set { 1, [#permalink] New post   03 Dec 2017, 18:54
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rxs0005 wrote:
If two different numbers are randomly selected from set { 1, 2, 3, 4, 5} what is the probability that the sum of the two numbers is greater than 4?


The number of ways to select 2 numbers from 5 is 5C2 = (5 x 4)/2! = 20/2 = 10.

To find the number of sums that are greater than 4, we can find the number of sums that ARE NOT greater than 4 and subtract that from 10.

1, 2

1, 3

So there are 10 - 2 = 8 sums that are greater than 4.

So the probability that the sum of the two numbers is greater than 4 is 8/10 = 4/5.
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Re: If two different numbers are randomly selected from set { 1, [#permalink] New post   04 Sep 2023, 14:06
A question for the experts: why are we not counting 2,2 as a non desirable outcome? Since we want sums greater than 4, shouldn't we be excluding 2,2 too? Making the answer B?
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Re: If two different numbers are randomly selected from set { 1, [#permalink]
04 Sep 2023, 14:06
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