A pair of dice are tossed. What is the probability that doubles are rolled, given that the sum on the two dice is less than 10? (Round your answer to three decimal places.)

To solve this problem, we first need to understand the total possible outcomes when two dice are rolled. Since a die has 6 faces, the total possible outcomes are 6*6 = 36.

Next, we need to find out the total outcomes where the sum of the two dice is less than 10. These are: (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (6,1), (6,2), (6,3), (6,4). That's a total of 30 outcomes.

Now, we need to find out the outcomes where doubles are rolled and the sum is less than 10. These are: (1,1), (2,2), (3,3), (4,4). That's a total of 4 outcomes.

The probability of an event is the number of ways that event can occur divided by the total number of outcomes. So, the probability that doubles are rolled given that the sum on the two dice is less than 10 is 4/30 = 0.133.

So, the answer is 0.133.