Nikki is spinning a spinner and rolling two dice what is the probability that she lands on a gray section of the spinner shown (a three-section circle with two of the sections grays and one white.) and rolls a sum of nine with the two dice show all of your work.
To find the probability of landing on a gray section of the spinner, we first need to determine the total number of equally likely outcomes. Since there are three sections on the spinner, the total outcomes are 3.
The probability of landing on a gray section is 2/3 (2 gray sections out of 3 total sections).
Next, we need to find the probability of rolling a sum of nine with two dice.
There are 36 possible outcomes when rolling two dice (6 sides on each die). To get a sum of nine, we can have the following combinations:
(3,6), (4,5), (5,4), (6,3)
So, there are 4 favorable outcomes out of 36 total outcomes.
The probability of rolling a sum of nine is 4/36, which simplifies to 1/9.
Finally, to find the probability of both events happening (landing on a gray section and rolling a sum of nine), we multiply the individual probabilities:
(2/3) * (1/9) = 2/27
Therefore, the probability that Nikki lands on a gray section of the spinner and rolls a sum of nine with two dice is 2/27.