Let's break down your questions step by step.
(a) Experimental Probability of Landing on Black
To calculate the experimental probability, you can use the formula:
\[ \text{Experimental Probability} = \frac{\text{Number of Spins for the Outcome}}{\text{Total Number of Spins}} \]
In this case, the number of spins for black is 11, and the total number of spins is 50. So:
\[ \text{Experimental Probability of Black} = \frac{11}{50} = 0.22 \]
Rounding to the nearest thousandth, the experimental probability of landing on black is 0.220.
(b) Theoretical Probability of Landing on Black
Since the spinner has 5 equally sized slices, and assuming it is fair, the theoretical probability can be calculated as:
\[ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{5} = 0.2 \]
(c) True Statement About Experimental vs. Theoretical Probabilities
The correct statement is:
As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
This reflects the Law of Large Numbers, which states that as you conduct more trials, the experimental probabilities will converge to the theoretical probabilities.
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