SOLUTION: Two ordinary fair, six-sided dice are rolled. What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 4?

Question 1129437: Two ordinary fair, six-sided dice are rolled.
What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 4?

What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 4?

What is the probability the sum of the numbers on the two dice is 9, given that it is not 4?

What is the probability exactly one of the dice shows the number 1 given that the sum of the numbers is 5?

Enter your answers as whole numbers or factions in lowest terms.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Given that one of the dice has to be a 4, the other has to be a 2 (1/6 probability).
Same for this with 4-4
Probability a sum is 9 is 4/36 (3-6,6-3,4-5,5-4). If the question is given that the number cannot be a 4. Given that a number is not 4, there are now 25 possible sums, and two of them are 9, 2/25 ANSWER
Given the sum is 5, there are 1-4,4-1,2-3,3-2, so given that the sum is 5, 1/2.
Probability is 1/2 that the exactly one of the dice shows a 1. The exactly doesn't matter, since both dice can't be 1.
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