Experimental Probability Statistics Example 3

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Example 3

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A spinner has sections coloured red, blue, and green. After 120 spins, the results are: Red 45, Blue 50, Green 25. (a) Find the experimental probability of each colour. (b) Do you think the spinner is fair (equal sections)? Justify your answer.

Solution

  1. 1
    Step 1: (a) P(R)=45120=0.375P(R) = \frac{45}{120} = 0.375, P(B)=50120โ‰ˆ0.417P(B) = \frac{50}{120} \approx 0.417, P(G)=25120โ‰ˆ0.208P(G) = \frac{25}{120} \approx 0.208.
  2. 2
    Step 2: (b) If the spinner were fair (3 equal sections), each probability would be 13โ‰ˆ0.333\frac{1}{3} \approx 0.333. Green's probability (0.208) is noticeably lower, suggesting the spinner is likely not fair โ€” the green section may be smaller.

Answer

(a) Red: 0.375, Blue: 0.417, Green: 0.208. (b) The spinner is likely not fair โ€” green appears significantly under-represented compared to the expected 13\frac{1}{3}.
Comparing experimental probabilities to expected theoretical values helps determine whether a device is fair. Large deviations from expected values suggest bias, though some variation is normal due to randomness. More trials increase our confidence in the conclusion.

About Experimental Probability

Experimental probability is the probability of an event estimated from actual experimental data, calculated as the number of times the event occurred divided by the total number of trials. It approaches the theoretical probability as more trials are conducted.

Learn more about Experimental Probability โ†’

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