A gambler rolls three fair six-sided dice. What is the

Hi VJesus12!

The total number of possible way: 6*6*6=216.
3 discs will appear in any one of the following arrangements: AAA, AAB, ABC, where AAA=All the same, AAB=Two are the same, ABC=All three different.

Now, the total number of AAA = 6.
The total number of ABC = 6*5*4 = 120.
Therefore, the total number of AAA, ABC = 126.

So, the total number of AAB = 216 - 126 = 90.
Probability of AAB = 90/216 = 5/12.

Regards!

VJesus12 wrote:A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?

A) 1/8
B) 5/18
C) 1/3
D) 5/12
E) 5/6

The total number of outcomes when 3 dice are rolled is 6 x 6 x 6 = 216.

We can use the following formula:

P(two of the dice show the same number, but the third shows a different number) =

1 - P(all three dice show the same number) - P(all three dice show a different number)

Now,

P(all three dice show a different number) = 6/6 x 5/6 x 4/6 = 20/36

and

P(all three dice show the same number) = 6/6 x 1/6 x 1/6 = 1/36

Thus,

P(two of the dice show the same number, but the third shows a different number) = 1 - 20/36 - 1/36 = 1 - 21/36 = 15/36 = 5/12

Answer: D