Problem

Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities. (Enter the probabilities as fractions.) (a) 10, given that a double was rolled (b) a double, given that an 10 was rolled

Solution

Step 1 :Suppose a pair of dice are rolled. We are to find the probabilities of the sum of the numbers on the top of the dice.

Step 2 :For part (a), we need to find the probability that the sum of the numbers on the dice is 10, given that a double was rolled. A double means that the numbers on both dice are the same. The only double that sums to 10 is a pair of 5s. There are 6 possible doubles (1-1, 2-2, 3-3, 4-4, 5-5, 6-6), so the probability is \(\frac{1}{6}\).

Step 3 :For part (b), we need to find the probability that a double was rolled, given that the sum of the numbers on the dice is 10. The doubles that sum to 10 are 5-5. There are three possible outcomes that sum to 10 (4-6, 5-5, 6-4), so the probability is \(\frac{1}{3}\).

Step 4 :Final Answer: (a) The probability that the sum of the numbers on the dice is 10, given that a double was rolled is \(\boxed{\frac{1}{6}}\).

Step 5 :(b) The probability that a double was rolled, given that the sum of the numbers on the dice is 10 is \(\boxed{\frac{1}{3}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/28888/

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