Let's break down the problem step-by-step and find the solutions to the questions provided.
(a) From Mary's results, compute the experimental probability of landing on blue.
The experimental probability is calculated by the ratio of the number of times the event occurs to the total number of trials.
Given:
- Number of blue spins (event occurring) = 6
- Total number of spins = 50
So, the experimental probability [tex]\( P(\text{blue}) \)[/tex] is:
[tex]\[
P(\text{blue}) = \frac{\text{Number of blue spins}}{\text{Total number of spins}} = \frac{6}{50} = 0.12
\][/tex]
Therefore, the experimental probability of landing on blue is [tex]\( 0.12 \)[/tex].
(b) Assuming that the spinner is fair, compute the theoretical probability of landing on blue.
The theoretical probability is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes, based on the setup of the spinner.
Given:
- Number of blue slices = 2
- Total number of slices = 4 (red) + 4 (yellow) + 2 (blue) = 10
So, the theoretical probability [tex]\( P(\text{blue}) \)[/tex] is:
[tex]\[
P(\text{blue}) = \frac{\text{Number of blue slices}}{\text{Total number of slices}} = \frac{2}{10} = 0.2
\][/tex]
Therefore, the theoretical probability of landing on blue is [tex]\( 0.2 \)[/tex].
(c) Assuming that the spinner is fair, choose the statement below that is true.
Given the nature of probabilities and the law of large numbers, with a smaller number of trials (spins), there's more variability in the experimental results compared to the theoretical probability. Hence, it is reasonable to expect deviations from the theoretical probability in small sample sizes.
The correct statement is:
- With a small number of spins, it is not surprising when the experimental probability is much less than the theoretical probability.
So the chosen statement is the second one:
[tex]\[
\text{With a small number of spins, it is not surprising when the experimental probability is much less than the theoretical probability.}
\][/tex]
