sandy wrote:
Damon rolls three six-sided dice. What is the probability that his total will be greater than 16 ?
Drill 3
Question: 4
Page: 528
There are FOUR ways to get a total that's greater than 16:
case i) 1st die is 5, 2nd die is 6 and 3rd die is 6 (aka 5-6-6)
case ii) 1st die is 6, 2nd die is 5 and 3rd die is 6 (aka 6-5-6)
case iii) 1st die is 6, 2nd die is 6 and 3rd die is 5 (aka 6-6-5)
case iv) 1st die is 6, 2nd die is 6 and 3rd die is 6 (aka 6-6-6)
case i:
P(1st die is 5
and 2nd die is 6
and 3rd die is 6) = P(1st die is 5)
x P(2nd die is 6)
x P(3rd die is 6)
= 1/6
x 1/6
x 1/6
=
1/216We can quickly see that P(case ii) =
1/216, P(case iii) =
1/216, and O(case iv) =
1/216So, P(sum greater than 16) = P(case i
OR case ii
OR case iii
OR case iv)
= P(case i)
+ P(case ii)
+ P(case iii)
+ P(case iv)
=
1/216 + 1/216 + 1/216 + 1/216= 4/216
ASIDE: On the GRE, we need not simplify our fractions.
So, entering 4/216 as our answer would be correct.
In fact, entering 40/2160 as our answer would also be correct.
Or, if we're so inclined, we can simplify 4/216 to get 1/54, which would also be correct.
Answer: 4/216 (aka 1/54)
Cheers,
Brent
6 5 6 can come twice right? 6 on First die and then third die and vice versa. If we consider repeated cases the probability will be 6/216. I know the answer would be wrong but just want to know why we are not considering it?
Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!