Nikki is spinning a spinner and rolling two dice what is the probability that she lands on a gray section of the spinner shown and rolls a sum of nine with the two dice show all of your work
First, let's determine the probability of landing on the gray section of the spinner. The spinner has 8 total sections, with two of them being gray. Therefore, the probability of landing on a gray section is 2/8 = 1/4.
Next, let's determine the probability of rolling a sum of nine with two dice. To do this, we need to consider all the possible outcomes when rolling two dice that result in a sum of nine. These outcomes are:
(3,6), (4,5), (5,4), (6,3)
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 nine is 4/36 = 1/9.
Finally, to find the overall probability of landing on a gray section of the spinner and rolling a sum of nine with the two dice, we multiply the individual probabilities:
P(gray section) * P(sum of nine) = (1/4) * (1/9) = 1/36
Therefore, the probability that Nikki lands on a gray section of the spinner and rolls a sum of nine with the two dice is 1/36.