Experimental Probability Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A bag contains an unknown number of red and blue marbles. In 80 draws (with replacement), 52 red and 28 blue marbles were drawn. (a) Estimate the probability of drawing a red marble. (b) If there are 20 marbles total, estimate how many are red.

Solution

  1. 1
    Step 1: (a) Experimental P(red)=5280=0.65P(\text{red}) = \frac{52}{80} = 0.65 or 65%.
  2. 2
    Step 2: (b) If P(red)≈0.65P(\text{red}) \approx 0.65 and there are 20 marbles, then estimated number of red marbles = 0.65×20=130.65 \times 20 = 13 red marbles.
  3. 3
    Step 3: This is an estimate — the actual number might be 12 or 14 due to sampling variability. More draws would give a more reliable estimate.

Answer

(a) P(red)≈0.65P(\text{red}) \approx 0.65. (b) Approximately 13 out of 20 marbles are red.
Experimental probability can be used to make predictions about unknown populations. By observing the relative frequency of outcomes in repeated trials, we can estimate the composition of the population. More trials lead to more accurate 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 3 medium

A spinner has sections coloured red, blue, and green. After 120 spins, the results are: Red 45, Blue

Example 4 hard

A basketball player made 72 out of 100 free throws in practice. (a) What is her experimental free-th

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