A pair of dice is tossed. Find the probability of the following. (Enter your probabilities as fractions.)

Question

(a)
Doubles are rolled.

B: The sum on the two dice is 10 and doubles are rolled.

C: The sum on the two dice is 10, given that doubles are rolled.

Answer 1

(a)
There are a total of 6 * 6 = 36 possible outcomes when rolling a pair of dice. Out of those, there are 6 outcomes where doubles are rolled (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).

So, the probability of rolling doubles is 6/36 = 1/6.

(b)
Out of the 36 possible outcomes, there are 3 ways to get a sum of 10 and doubles rolled (4-6, 5-5, 6-4).

So, the probability of getting a sum of 10 and doubles rolled is 3/36 = 1/12.

(c)
Since we are given that doubles are rolled, the only possible outcomes are the 6 doubles mentioned in part (a). Out of these, only 1 doubles pair (5-5) has a sum of 10.

So, the probability of getting a sum of 10, given that doubles are rolled, is 1/6.

Answer 2

this is incorrect

Answer 3

I apologize for the mistake. Let me correct it:
(a) Number of ways to roll doubles = 6 (1-1, 2-2, 3-3, 4-4, 5-5, 6-6)
Total number of outcomes = 36
Probability of rolling doubles = 6/36 = 1/6

(b) Number of ways to get a sum of 10 and doubles rolled = 1 (5-5)
Probability of getting a sum of 10 and doubles rolled = 1/36

(c) Probability of rolling doubles and getting a sum of 10 = 1/6 * 1/6 = 1/36

So the corrected probabilities are:
(a) 1/6
(b) 1/36
(c) 1/36