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?

Explanation:

Identify the sample space and outcomes

Using the Theoretical Probability knowledge point
The fair spinner has four equal-sized sectors colored yellow, blue, green, and red.
The total number of possible outcomes is \(4\).
The probability of spinning any single color (such as yellow or green) is:

$$ P(\text{yellow}) = \frac{1}{4}, \quad P(\text{green}) = \frac{1}{4} $$

Apply the addition rule for mutually exclusive events

Using the Probability Addition Rule and Mutually Exclusive Events knowledge points
Since the spinner can only land on one color at a time, spinning a yellow and spinning a green are mutually exclusive events.

$$ P(\text{yellow or green}) = P(\text{yellow}) + P(\text{green}) = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $$

Answer:

What is the probability of spinning a yellow or a green?
<blank>\(\frac{1}{2}\)</blank>