Answer:
To solve this problem, we will use the following steps:
Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).
Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.
Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.
Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.
Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.
Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.
Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.
Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.
5/18 = 0.278
Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.