To solve this problem, we need to fill in the required probabilities and analyze the statements based on the outcomes of the spinner.
(a) Theoretical Probability of Landing on White
Since there are 10 equally sized slices on the spinner and one of them is white:
\[ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{10} = 0.1 \]
(b) Experimental Probability of Landing on White
From Elsa's results, the number of spins that resulted in white is 498 out of a total of 1000 spins. Therefore, the experimental probability is calculated as follows:
\[ \text{Experimental Probability} = \frac{\text{Number of spins landing on white}}{\text{Total spins}} = \frac{498}{1000} = 0.498 \]
(c) Statement Analysis
Now, we examine the statements provided:
- The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
- The smaller the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
- The experimental probability will never be very close to the theoretical probability, no matter the number of spins.
The correct statement is:
- The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
This is based on the Law of Large Numbers, which states that as the number of trials increases, the experimental probability will converge towards the theoretical probability.
Summary of Answers:
(a) 0.1
(b) 0.498
(c) The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.