1. ## Probability.......Average

3 positive integers are selected at random from 9 consecutive positive integers. What is the probability that their average is also an integer.

a) 9/28

b) 1/28

c) 1/3

d) 5/14

e) 9/29

SPOILER: D  Reply With Quote

2. Centrino .. where did you get this question.. seems to be HARDDDDDDDDDDDDDDDD BIN ...

struggled for sometime but think this is the approach... i got the answer with this approach..

the 9 numbers are
3 are in the form 3n ( multiples of 3) ---- SET 1
3 are in the form 3n+1 ---- SET 2
3 are in the form 3n+2 ---- SET 3

if you take the 3 numbers from the same set then the sum is divisible by 3 ..
so we got 3 combinations here for 3 sets ..
the only other way is taking 1 from each set ... so 3C1 * 3C1 * 3C1 = 27
[ this is like 3n + 3n+1+3n+2 = 9n+3 which is divisible by 3]
so total combinations = 3+27 = 30

probability = 30/84 = 5/14

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3. Many thanks Chix.........I liked your logic.  Reply With Quote

4. It's probably the hardest probability problem. Is there any easier approach?  Reply With Quote