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.

Explanation:

Analyze the spinner properties

Using the Theoretical Probability knowledge point
The problem states that we have a "fair spinner" with four possible outcomes, one for each color shown in the image (green, red, blue, yellow). Since the spinner is fair and divided into four equal quadrants, each color has an equal probability of being landed on:

$$ P(\text{Green}) = P(\text{Red}) = P(\text{Blue}) = P(\text{Yellow}) = \frac{1}{4} $$

Determine the distribution type

Using the Probability Distribution knowledge point
Since the probability of each of the four outcomes is equal, the outcomes are equally likely. A probability distribution where all outcomes have the same probability is called a uniform probability distribution. Therefore, the statements "The probability of each outcome is equal" and "The outcomes have a uniform probability distribution" are true, while the other two statements are false.

Answer:

• The probability of each outcome is equal (Correct answer)
• The probability of each outcome is different.
• The outcomes have a uniform probability distribution. (Correct answer)
• The outcomes have a nonuniform distribution.