Question

the fair spinner shown is spun 1 time. there are four possible outcomes, one for each color. based on the picture, which statements are true?
the probability of each outcome is equal
the probability of each outcome is different.
the outcomes have a uniform probability distribution.
the outcomes have a nonuniform distribution
what is the probability of spinning a yellow?
1/4
complete
what is the probability of spinning a yellow or a green?
0.5
complete
what is the sum of the probabilities for all possible outcomes?

Explanation:

Step1: Calculate probability of each outcome

Since there are 4 equal - sized sections (yellow, blue, green, red) on the spinner, the probability of each outcome \(P(\text{each color})=\frac{1}{4}\)

Step2: Calculate probability of yellow or green

Using the formula \(P(A\cup B)=P(A)+P(B)\) (where \(A\) is spinning yellow and \(B\) is spinning green). \(P(\text{yellow})=\frac{1}{4}\), \(P(\text{green})=\frac{1}{4}\), so \(P(\text{yellow}\cup\text{green})=\frac{1 + 1}{4}=\frac{2}{4}=0.5\)

Step3: Calculate sum of probabilities of all outcomes

By the property of probability distribution, for a sample space \(S\) with \(n\) mutually - exclusive and exhaustive events \(E_1,E_2,\cdots,E_n\), \(\sum_{i = 1}^{n}P(E_i)=1\). Here \(n = 4\) and \(P(\text{yellow})=P(\text{blue})=P(\text{green})=P(\text{red})=\frac{1}{4}\), so \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=1\)

Answer:

\(1\)