a. List the sample space for spinning arrows (not shown) on the three spinners shown. Find each probability.

b. P(all the same color or red on one of the spinners)

c. P(yellow on all three spinners or red on all three spinners)

d. P(blue on at least one spinner or yellow on at least one spinner)

Solution

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a) Sample space for a process or experiment is the set of all the possible outcomes for the process or the experiment. Sample space for the first spinner is $\{\text{B,R,Y,G}\}$ . Probabilities of all the events in a sample space must add up to $1$ so, since the sections of the spinner in the picture are the same size, we know that the outcomes are equally likely, the probability of each of the outcomes is equal to $\frac{1}{4}$ .
Sample space for the second spinner is $\{\text{B,G,Y}\}$ . Probabilities of all the events in a sample space must add up to $1$ so, since the sections of the spinner in the picture are the same size, we know that the outcomes are equally likely, the probability of each of the outcomes is equal to $\frac{1}{3}$ .
Sample space for the third spinner is $\{R,Y\}$ . Again, because the sections of the spinner in the picture are the same size, we know that the outcomes are equally likely. The probability of each of the outcomes is equal to $\frac{1}{2}$ .