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ps- VERY NICE- NUMBER PROPERTIES [#permalink]
11 Jun 2007, 09:12
0% (00:00) correct
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If two integers between –5 and 3, inclusive, are chosen at random, which of the following is most likely to be true?
(A) The sum of the two integers is even
(B) The sum of the two integers is odd
(C) The product of the two integers is even
(D) The product of the two integers is odd
(E) The product of the two integers is negative
Between -5 and 3 (inclusive) there are 6 odd numbers -5.-3,-1,1,3 and there are 4 evens -4,-2,2
There are 5 negative and 3 positive numbers
I am tempted to intuitively say that product of 2 integers being even seems to be the best bet, but lets check the probabilities in detail :
A) happens when both numbers are odd or both are even : 6/10*5/9 + 4/10*3/9 = 7/15
B) happens if one odd and one even 6/10*4/9+4/10*6/9=9/15
C)happens when one of the numbers is even = 1- P(both are odd)
= 1 - ( 6/10 * 5/9) = 1-1/3 - 2/3 = 10/15
D)happens when both numbers are odd = 6/10 * 5/9 =1/3 or 5/15
E) happens when one of the numbers is <0>=0) = 1 - (4/10*3/9) = 13/15 --> AHA moment