Question

Brian rolls a number cube twice. what is the probability that the sum of the 2 rolls is less than 6, given that the first roll is a 3? a. one over six b. one over three c. one over two d. two over three

Answer 1

Given that the first roll is a 3, we want to find the sum of 3 and the second roll:

If the second roll is 1, then the sum is 3 + 1 = 4.

If the second roll is 2, then the sum is 3 + 2 = 5.

If the second roll is 3, then the sum is 3 + 3 = 6.

If the second roll is 4, then the sum is 3 + 4 = 7.

If the second roll is 5, then the sum is 3 + 5 = 8.

If the second roll is 6, then the sum is 3 + 6 = 9.

Now, we can see that there are two outcomes (rolls of 1 and 2) that result in a sum of less than 6 out of a total of six possible outcomes for the second roll. So, the probability of getting a sum less than 6, given that the first roll is a 3, is:

(Number of favorable outcomes) / (Total number of possible outcomes) = 2 / 6 = 1/3.

So, the answer is (b) one over three.