Question

answer the following. round your answers to the nearest thousandths.
(a) from martinas results, compute the experimental probability of landing on yellow.
(b) assuming that the spinner is fair, compute the theoretical probability of landing on yellow.
(c) assuming that the spinner is fair, choose the statement below that is true.
the experimental and theoretical probabilities must always be equal.
as the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
as the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.
a spinner with 10 equally - sized slices has 5 yellow slices, 3 red slices, and 2 blue slices. martina spun the dial 20 times and got the following results:

outcome	number of spins
red	12
blue	2

Explanation:

Step1: Calculate experimental probability

Experimental probability = $\frac{\text{Number of times yellow occurred}}{\text{Total number of spins}}$. Total number of spins is $6 + 12+2=20$, and number of times yellow occurred is 6. So experimental probability of landing on yellow is $\frac{6}{20}= 0.3$.

Step2: Calculate theoretical probability

The spinner has 10 equally - sized slices with 5 yellow slices. Theoretical probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So theoretical probability of landing on yellow is $\frac{5}{10}=0.5$.

Step3: Analyze statement in part (b)

The statement "Assuming that the spinner is fair, the experimental and theoretical probabilities must always be equal" is false. In probability, as the number of trials (spins in this case) increases, the experimental probability gets closer to the theoretical probability, but for a small number of trials, they can be different.

Answer:

(a) 0.3
(b) False
(c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.