Probability need help

Hi Winner2013,

This question layers on the details, so you have to be very careful with how you organize it. There are a couple of different ways to do the math, but here's a way that allows you to see all of the possibilities:

First, let's deal with the fact that even numbers appear 4x as frequently as odd numbers.

Roll
1 x 1
2 x 4
3 x 1
4 x 4
5 x 1
6 x 4

Total possible outcomes per roll = 15

Now, we need to calculate the probability of what we WANT (a three-roll sum > 16): So, we need a total of 17 or 18.

To get a 17 or 18, we need one of the following possibilities:
665
656
566
666

Odds of 665: (4/15)(4/15)(1/15) = 4^2/15^3
Odds of 656: Same as above = 4^2/15^3
Odds of 566: Same as above = 4^2/15^3

Odds of 666: (4/15)(4/15)(4/15) = 4^3/15^3

Total odds: 16(3) + 64 = 112/15^3

Final Answer: 4

GMAT assassins aren't born, they're made,
Rich

Hi Winner2013,

The reason why your logic didn't quite work in this question is that you did not account for ALL of the numbers. To score 17 or 18 on three rolls, you CAN'T have any 1s, 2s, 3s or 4s. Your math doesn't account for that; it only accounts for the probability of rolling an odd (1/5) vs. rolling an even (4/5).

You DID correctly deduce that there are 3 ways to roll 17 and 1 way to roll 18. To adjust your calculation, you have to consider ALL the possible outcomes (so you divide each value by 15, not 5).

GMAT assassins aren't born, they're made,
Rich