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# Two numbers are randomly selected without replacement

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Two numbers are randomly selected without replacement from the first 12 positive integers. Find the probability that the sum of these two numbers is 10.

a) 7/144

b) 1/24

c) 1/18

d) 5/144

e) 1/16

Guest Dec 16, 2017
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#1
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The denominators that you have indicate that this is probably  with replacement

The number of possible sums  without replacement are  12 * 11   =  132

Sums of 10  =

1   9

9   1

2   8

8   2

7   3

3   7

4   6

6   4

So.......the probability that the numbers sum to 10  without replacement is just    8  / 132   =  2 / 33

However.....with replacement we have    12  * 12   =  144 possible sums

1   9

9   1

2   8

8   2

7   3

3   7

4   6

6   4

5   5

So....the probability  that we have a sum of 10 with replacement is just   9  / 144   =  1  / 16

CPhill  Dec 16, 2017
edited by CPhill  Dec 16, 2017

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