Experimental Probability Statistics Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA basketball player made 72 out of 100 free throws in practice. (a) What is her experimental free-throw probability? (b) In the next game, she attempts 15 free throws. How many would you expect her to make? (c) Why might the actual number differ from your prediction?
Solution
- 1 Step 1: (a) . (b) Expected makes = free throws.
- 2 Step 2: (c) The actual number may differ because: (1) 15 attempts is a small sample size with high variability, (2) game pressure differs from practice, (3) experimental probability is an estimate and individual attempts are independent random events.
Answer
(a) . (b) Expected: about 11 free throws. (c) Small sample size, game pressure, and randomness may cause the actual result to differ.
Experimental probability provides estimates useful for prediction, but predictions are uncertain, especially with small sample sizes. Real-world factors (pressure, fatigue) may also cause actual performance to deviate from practice-based estimates.
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 →More Experimental Probability Examples
Example 1 easy
A student flips a coin 50 times and gets 28 heads and 22 tails. What is the experimental probability
Example 2 mediumA bag contains an unknown number of red and blue marbles. In 80 draws (with replacement), 52 red and
Example 3 mediumA spinner has sections coloured red, blue, and green. After 120 spins, the results are: Red 45, Blue