Question

properties of probability distributions
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? choose two correct answers.
the probability of each outcome is equal.
the outcomes have a uniform probability distribution.
the probability of each outcome is different.
the outcomes have a nonuniform distribution.

Explanation:

1. For "The probability of each outcome is equal": A fair spinner with equal - sized sections (the four color sections here look equal) means each outcome (landing on a color) has the same probability. Since there are 4 outcomes, the probability for each is $\frac{1}{4}$.
2. For "The outcomes have a uniform probability distribution": A uniform probability distribution is one where each outcome has an equal probability of occurring. Since each color outcome has the same probability (as the sections are equal), the outcomes follow a uniform distribution.
3. For "The probability of each outcome is different": This is false because the spinner is fair and the sections are equal, so probabilities should be equal.
4. For "The outcomes have a nonuniform distribution": This is false because non - uniform distribution implies different probabilities for different outcomes, which is not the case here.

Answer:

• The probability of each outcome is equal.
• The outcomes have a uniform probability distribution.