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Set A and B (Posted on 2002-05-29) Difficulty: 3 of 5
Consider the following two sets:

Set A = { 2,3,4,6 }
Set B = { 2,5,7,9 }

What is the probability that two randomly chosen elements from B would add up to be more than the product of two randomly chosen elements from A?

  Submitted by Dulanjana    
Rating: 2.5000 (8 votes)
Solution: (Hide)
There are six ways to pick a pair of numbers from a set of four. For set A, the possible pairs and their products are:
  • (2*3) = 6
  • (2*4) = 8
  • (2*6) = 12
  • (3*4) = 12
  • (3*6) = 18
  • (4*6) = 26

    For set B, the pairs and their sums are:

  • (2+5) = 7
  • (2+7) = 9
  • (2+9) = 11
  • (5+7) = 12
  • (5+9) = 14
  • (7+9) = 16

    Out of the possibilities listed, the outcomes where the sum of a pair from B is greater than a product of a pair from A is as follows:

  • Product of A is 6: Sum of B can be 7, 9, 11, 12, 14 and 16
  • Product of A is 8: Sum of B can be 9, 11, 12, 14 and 16
  • Product of A is 12 (2*6): Sum of B can be 14 and 16
  • Product of A is 12 (3*4): Sum of B can be 14 and 16
  • Product of A is 18 or 24: No pair from B will result in a greater sum.

    In all, we have 6+5+2+2 = 15 possibilities to meet the condition required, out of a total 36 possible outcomes. This the probability is 15/36

  • Comments: ( You must be logged in to post comments.)
      Subject Author Date
    SolutionAnswerPraneeth2007-08-23 07:13:58
    answer to the problemK Sengupta2007-03-09 05:22:12
    SolutionI concur with the originalTristan2003-04-26 11:51:46
    answer maybeluvya20032003-03-15 10:04:46
    re: AAaarrghhh!levik2002-05-29 19:17:54
    AAaarrghhh!TomM2002-05-29 17:11:52
    Brute ArithmaticTomM2002-05-29 17:03:31
    Early thoughtsTomM2002-05-29 16:47:20
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