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ps- VERY NICE- NUMBER PROPERTIES [#permalink]
11 Jun 2007, 09:12

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Question Stats:

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0% (00:00) wrong based on 0 sessions

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

Now, lets calculate the probablity or the likelyhood of each event:

(A) The sum of the two integers is even That'll be when picking 2 odds or 2 evens
P(A)= 5/9 x 4/8 + 4/9 x 3/8 = 32/72 = 4/9

(B) The sum of the two integers is odd That holds when picking 1 odd and 1 even
P(B) = 5/9 x 4/8 + 4/9 x 5/8 = 2 x 20/72 = 40/72 = 5/9

(C) The product of the two integers is even That'll be true when picking eithe 1 even 1 odd or 2 evens.
P(C) = P(B) + 4/9 x 3/8 = 5/9 + 12/72 = 5/9 + 1/6 = 39/54

(D) The product of the two integers is odd That holds when picking two odds only ..
P(D) = 5/9 x 4/8 = 20/72 = 5/18 = 2.5/9

(E) The product of the two integers is negative that holds when picking one negative and one positive
P(E) = 5/9 x 3/8 + 3/9 x 5/8 = 30/72 = 5/12

Yahoooo. My first glence worked out perfectly and my stats courses in college are helping me now ..
39/54 has the largest value among all answer choices.