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?

what is the probability of spinning a yellow or a green?

what is the sum of the probabilities for all possible outcomes?

Explanation:

Identify the sample space and outcomes

Using the Sample Space Probability knowledge point
The spinner is divided into four equal sectors: yellow, blue, green, and red. Since the spinner is fair, each of these four outcomes is equally likely.

Apply probability axioms for the sum

Using the Probability Axioms knowledge point

$$ \sum P(X_i) = P(\text{yellow}) + P(\text{blue}) + P(\text{green}) + P(\text{red}) = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = 1 $$

Answer:

What is the sum of the probabilities for all possible outcomes? <blank>1</blank>