Nikki is rolling two dice. What is the probability that she rolls a sum of 4 with the two dice, then rolls a sum of 7 with the two dice? Show all your work.
To find the probability of rolling a sum of 4 with two dice, we first need to determine the number of ways to get a sum of 4.
The possible combinations that result in a sum of 4 are (1,3), (2,2), and (3,1). There are a total of 36 possible outcomes when rolling two dice (6 sides on each die), so the probability of rolling a sum of 4 is 3/36 or 1/12.
Next, we need to find the probability of rolling a sum of 7 with two dice. The combinations that result in a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 ways to get a sum of 7 out of 36 possible outcomes, so the probability of rolling a sum of 7 is 6/36 or 1/6.
To find the probability of rolling a sum of 4 and then rolling a sum of 7, we multiply the probabilities of each event happening consecutively:
1/12 (probability of rolling a sum of 4) * 1/6 (probability of rolling a sum of 7) = 1/72
So, the probability of Nikki rolling a sum of 4 with the two dice, then rolling a sum of 7 with the two dice is 1/72.