Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Experimental Probability.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
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.
You flip a coin 100 times and get 53 heads. Your experimental probability is 10053=0.53. It's based on what DID happen, not what should happen theoretically.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Experimental Probability starts by naming the possible outcomes and the event rule before assigning or combining probabilities.
Common stuck point:Students often know a procedure related to experimental probability but skip the recognition step: Am I reasoning about what can happen and how likely it is, with the correct sample space or condition? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I reasoning about what can happen and how likely it is, with the correct sample space or condition?
Worked Examples
Example 1
medium
A factory tests 400 widgets; 12 fail. Predict the expected number of failures in a batch of 3000.
Answer
90 failures
First step
1
Failure rate: 40012=0.03.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A game shows: in 800 plays a special bonus triggered 56 times. Estimate P(bonus) as a percentage.
Example 3
hard
Two students each track a coin: Alex flips 30 times and sees 20 heads; Bri flips 300 times and sees 165 heads. Whose experimental probability is closer to the theoretical 21?
Example 4
challenge
Two trials of 100 spins each give red counts of 28 and 34. Combine them: what is the pooled experimental probability of red?Two trials of 100 spins each — red counts
Example 5
easy
A student flips a coin 50 times and gets 28 heads and 22 tails. What is the experimental probability of getting heads?
Example 6
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.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A coin is flipped 20 times and lands heads 12 times. What is the experimental probability of heads?20 flips: 12 heads, 8 tails
Example 2
easy
A die is rolled 30 times and shows a 5 a total of 6 times. What is the experimental probability of rolling a 5?
Example 3
easy
In 50 free throws a player makes 35. What is the experimental probability of making a free throw?
Example 4
easy
A spinner is spun 40 times and lands on red 10 times. What is the experimental probability of red?40 spins: 10 red, 30 not red
Example 5
easy
A bag is sampled with replacement 25 times; a blue marble appears 5 times. What is the experimental probability of blue?
Example 6
easy
A number cube is rolled 100 times; an even number comes up 48 times. What is the experimental probability of an even number?
Example 7
easy
A weather log shows rain on 9 of the last 30 days. What is the experimental probability of rain?
Example 8
easy
A quiz tracks 60 attempts at a problem with 45 correct. What is the experimental probability of a correct attempt?
Example 9
medium
A die rolled 60 times shows a 3 exactly 8 times. By how much does the experimental probability of a 3 differ from the theoretical probability?
Example 10
medium
A spinner lands on green 18 times in 45 spins. Based on this, how many green landings are expected in 100 spins?
Example 11
medium
A bag is sampled with replacement 80 times; red appears 32 times. Estimate how many of 25 marbles are red.
Example 12
medium
Over 200 trials an event occurs 50 times. What is the experimental probability as a decimal?
Example 13
medium
Two students test a coin. Student A gets 6 heads in 10 flips; Student B gets 52 heads in 100 flips. Whose experimental probability is closer to the theoretical 21?
Example 14
medium
A factory inspects 500 items and finds 15 defective. What is the experimental probability an item is defective, as a percent?
Example 15
medium
A die showed these counts in 60 rolls: 1:9, 2:11, 3:10, 4:8, 5:12, 6:10. What is the experimental probability of rolling a 5?
Example 16
medium
In 80 spins a spinner lands red 24 times. What is the experimental probability of red as a decimal?
Example 17
medium
A machine produces 400 parts with 12 defects. Based on this rate, how many defects are expected in 1000 parts?
Example 18
challenge
A coin is flipped n times and lands heads 21 times, giving an experimental probability of 0.42. Find n.
Example 19
challenge
A spinner's experimental probability of blue is 83 from 160 spins. The next 40 spins give 20 blues. What is the combined experimental probability of blue?
Example 20
challenge
A die is rolled 120 times. If the experimental probability of an even number is 157, how many even rolls occurred?
Example 21
easy
A spinner is spun 80 times and lands on green 24 times. What is the experimental probability of landing on green?80 spins: 24 green, 56 not green
Example 22
easy
Out of 150 light bulbs tested, 6 were defective. What is the experimental probability that a bulb is defective?
Example 23
easy
A bag is sampled with replacement 40 times; a yellow marble appears 16 times. What is the experimental probability of yellow?40 samples: 16 yellow, 24 other
Example 24
easy
A school survey finds 90 of 300 students walk to school. What is the experimental probability a student walks?
Example 25
easy
In a video game, a chest contains gold in 84 of the first 240 opens. What is the experimental probability of finding gold?
Example 26
easy
A die is rolled 36 times and lands on a 6 seven times. What is the experimental probability of rolling a 6?
Example 27
medium
A spinner lands on red 36 times in 120 spins. Predict the number of red landings in 500 spins.
Example 28
medium
A coin lands heads 27 times in 50 flips. By how much (as a decimal) does the experimental probability differ from the theoretical probability?
Example 29
medium
A bag of unknown marbles is sampled with replacement 150 times; blue marbles appear 60 times. Estimate how many of the 25 marbles in the bag are blue.
Example 30
medium
A die is rolled 200 times; even numbers come up 90 times. What is the experimental probability of an odd number?
Example 31
medium
A spinner shows red, blue, or green. In 250 spins: red 80, blue 95, green 75. What is the experimental probability of blue?
Example 32
medium
Over 60 archery shots, 27 hit the bullseye. Predict the number of bullseyes in the next 100 shots.
Example 33
hard
A trial set: 1200 spins, red 280, blue 360, green 560. Find the experimental probability of NOT green.1200 spins — counts per color; find P(not green)
Example 34
hard
A coin lands heads 600 times in 1000 flips. If the next 200 flips continue at the same rate, how many additional heads would you predict?
Example 35
hard
A die rolled 250 times shows a 6 forty-five times. If the die is fair, what is the difference between observed and theoretical probability?
Example 36
hard
A library tracks 480 returned books; 36 were overdue. Predict the number of overdue books out of 2000 returns.
Example 37
hard
A coin flipped 80 times shows heads 56 times. Is this experimental probability more, less, or equal to 21?
Example 38
challenge
A weighted die rolls a 6 in 90 of 360 rolls. Assuming the rate continues, how many sixes are expected in 1000 rolls, and how much higher is this rate than a fair die's expected count?
Example 39
medium
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.
Example 40
hard
A 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?