SOLUTION: Two integers are randomly selected from the set​ {1, 2,​ 3, 4,​ 5, 6,​ 7, 8,​ 9} and are added together. Find the probability that their sum is 16 if they are selected

Algebra ->  Probability-and-statistics -> SOLUTION: Two integers are randomly selected from the set​ {1, 2,​ 3, 4,​ 5, 6,​ 7, 8,​ 9} and are added together. Find the probability that their sum is 16 if they are selected      Log On


   

Question 1198097: Two integers are randomly selected from the set​ {1, 2,​ 3, 4,​ 5, 6,​ 7, 8,​ 9} and are added together. Find the probability that their sum is 16 if they are selected
Answer by math_helper(2461) About Me  (Show Source):
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         1    2    3    4    5    6    7    8    9



  1      2    3    4    5    6    7    8    9    10

  2      3    4    5    6    7    8    9    10   11

  3      4    5    6    7    8    9    10   11   12

  4      5    6    7    8    9    10   11   12   13

  5      6    7    8    9    10   11   12   13   14

  6      7    8    9    10   11   12   13   14   15

  7      8    9    10   11   12   13   14   15   16 

  8      9    10   11   12   13   14   15   16   17

  9      10   11   12   13   14   15   16   17   18





If the numbers are chosen with replacement (such as picking one ball from a jar of nine, each labeled with the digits 1..9, and then replacing the first ball before drawing the 2nd), you get P(sum=16) = 3/81 = 1/27 which is approximately 0.037.



If the numbers are chosen without replacement (such as taking two balls out of a jar of nine balls each labeled with one of the above digits) then there are only two ways (7 & 9, or 9 & 7), out of 9*8=72 outcomes, to get a sum of 16.  In this scenario, P(sum=16) = 2/72 = 1/36 or approximately 0.028.