Final answer:
The probability distribution for the random variable "yellow (Y)" when Joaquin spins the spinner twice is: P(0 yellows) = 0.75, P(1 yellow) = 0.1875, P(2 yellows) = 0.0625.
Step-by-step explanation:
To determine the correct probability distribution for the random variable "yellow (Y)" when Joaquin spins the spinner twice, we start by examining the set of outcomes S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}. We count the occurrences of the results that include yellow:
- One yellow (YR, YB, YG) - 3 outcomes
- Two yellows (YY) - 1 outcome
- No yellows (all other combinations) - 12 outcomes
Since there are 16 total outcomes and each outcome is equally likely, we can find the probability of getting yellows as follows:
- P(0 yellows) = Number of outcomes without yellows / Total number of outcomes = 12/16 = 0.75
- P(1 yellow) = Number of outcomes with one yellow / Total number of outcomes = 3/16 = 0.1875
- P(2 yellows) = Number of outcomes with two yellows / Total number of outcomes = 1/16 = 0.0625
Therefore, the probability distribution for the random variable "yellow" is:
- P(0 yellows) = 0.75
- P(1 yellow) = 0.1875
- P(2 yellows) = 0.0625