# A die is rolled thrice

• Sep 9th 2013, 04:46 AM
usre123
A die is rolled thrice
three dice are thrown. what is the probability that the first two show the same number, and the last one a different number?

So I did 1/6 * 1/6 * 5/6 (first two show the same number, the last one another number) = 5/216. then i multiply by 3 and get 15/216. the answer is 15/36. why?
Thanks!
• Sep 9th 2013, 06:33 AM
Plato
Re: A die is rolled thrice
Quote:

Originally Posted by usre123
three dice are thrown. what is the probability that the first two show the same number, and the last one a different number?
So I did 1/6 * 1/6 * 5/6 (first two show the same number, the last one another number) = 5/216. then i multiply by 3 and get 15/216. the answer is 15/36. why?

Why do you think that the answer is 15/36?

As you noted there are 216 possible triples.

How many of those look like $\displaystyle (X,X,Y)$ where $\displaystyle X\ne Y~?$.

Divide that number by 216.
• Sep 9th 2013, 08:39 AM
HallsofIvy
Re: A die is rolled thrice
The "probability the first two show the same number" is NOT "1/6*1/6". That is the probability that the first two numbers are a specific number from 1 to 6. Here, the first two numbers can be any number 1 to 6 as long as they are the same. The first number can be any number. The probability of that is, of course, 1. Then the second number must be the same as the first- the probability of that is 1/6 to the probability that the first two numbers are the same is 1(1/6)= 1/6.
• Sep 10th 2013, 01:21 AM
usre123
Re: A die is rolled thrice
the official answer is 15/36. I'm at a loss. I get 5/216
• Sep 10th 2013, 03:07 AM
Plato
Re: A die is rolled thrice
Quote:

Originally Posted by usre123
the official answer is 15/36. I'm at a loss. I get 5/216

Of the 216 triples, there are 30 with the form $\displaystyle (X,X,Y)$ where $\displaystyle X\ne Y~.$

That gives the probability $\displaystyle \frac{30}{216}=\frac{5}{36}$.

It seems that the given answer is incorrect.
That a suggested answer is for the question: The probability that two of the dice are equal and the third different.
Did you translate the question correctly?