perplexus.info :: Probability : Set A and B

Set A and B (Posted on 2002-05-29)

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
Answer	Praneeth	2007-08-23 07:13:58
answer to the problem	K Sengupta	2007-03-09 05:22:12
I concur with the original	Tristan	2003-04-26 11:51:46
answer maybe	luvya2003	2003-03-15 10:04:46
re: AAaarrghhh!	levik	2002-05-29 19:17:54
AAaarrghhh!	TomM	2002-05-29 17:11:52
Brute Arithmatic	TomM	2002-05-29 17:03:31
Early thoughts	TomM	2002-05-29 16:47:20

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