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Probability Question

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by thashadow » Wed Nov 03, 2010 8:24 am
Hey guys, long time reader, first time poster. I couldn't figure this one out, so of course I come to you guys to walk me through the steps. Have a go at it.

X - {1,2,3,4,5}
Y - {1,2,3,4,5}

Randomly pick one number from Set x, and one number from set Y

What is the probability that the product of x and y is less than 10?


Thanks
-L
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by Rahul@gurome » Wed Nov 03, 2010 9:10 am
thashadow wrote:Hey guys, long time reader, first time poster. I couldn't figure this one out, so of course I come to you guys to walk me through the steps. Have a go at it.

X - {1,2,3,4,5}
Y - {1,2,3,4,5}

Randomly pick one number from Set x, and one number from set Y

What is the probability that the product of x and y is less than 10?


Thanks
-L
Total number of possible pairs = 5 + 5 + 5 + 5 + 5 = 25

Total number of pairs such that, xy < 10:
  • (1) x = 1, y can be 1, 2, 3, 4 or 5 --> 5 ways
    (2) x = 2, y can be 1, 2, 3 or 4 --> 4 ways
    (3) x = 3, y can be 1, 2 or 3 --> 3 ways
    (4) x = 4, y can be 1 or 2 --> 2 ways
    (5) x = 5, y can be 1 --> 1 way
Thus a total of = 5 + 4 + 3 + 2 + 1 = 15 ways.

Therefore, required probability = 15/25 = 3/5
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by gtestprep » Wed Nov 03, 2010 9:16 am
So let's assume there are 2 slots that need to be filled up such that the first slot is always filled with a number from Set X and the second slot from Set Y. If you selected 1 from Set X, then there are 5 ways to select an element from Set Y such that the product of the numbers is less than 10. So, there are 5 ways of doing this ( 1*1, 1*2, 1*3, 1*4 and 1*5 )

Likewise, if you selected 2 from Set X, then there are 4 ways to select an element from Set Y (remember 2 * 5 = 10) There are 4 ways of doing this ( 2*1, 2*2, 2*3 and 2*4 )

Similarly, if 3, 4 and 5 are selected from Set X, there are 3, 2 and 1 ways respectively (such that the product is less than 10)

Therefore, the total number of ways of selecting elements from set X & Y such that the product of both the elements is less than 10 is the sum of the individual possibilities as stated above. i.e. 5 + 4 + 3 + 2 + 1 = 15

The total number of ways of selecting the numbers though is 5 from set X and 5 from set Y. So, there are 25 total ways of selecting numbers.

The probability is 15/25 = 3/5

HTH
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