A spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}. If the random variable is “yellow (Y),” which of the following is the correct probability distribution?
To determine the probability distribution for the random variable "yellow (Y)," we need to determine the number of times Y occurs in the set of outcomes and calculate the probability.
First, let's count the number of times Y occurs in the set S: YR, YB, YG, and YY. So, Y occurs 4 times in the set.
Next, we calculate the probability of Y occurring by dividing the number of times Y occurs by the total number of possible outcomes. Since the spinner is spun twice, there are 4 sections in each spin, resulting in a total of 4 * 4 = 16 possible outcomes. Therefore, the probability of Y occurring is 4/16 = 1/4 or 0.25.
Now, we can construct the probability distribution table for the random variable "yellow (Y)":
Y | Probability
----------------------
YR | 1/16
YB | 1/16
YG | 1/16
YY | 1/16
So, the correct probability distribution for the random variable "yellow (Y)" is:
YR with probability 1/16
YB with probability 1/16
YG with probability 1/16
YY with probability 1/16