Theoretical vs Experimental Probability
Compare expected chances with real results
Theoretical vs Experimental Probability
Compare expected chances with real results
Math - Grade 6-8
- 1
A fair number cube has faces numbered 1 through 6. What is the theoretical probability of rolling a 4?
Theoretical probability uses what should happen in a fair situation.
The theoretical probability of rolling a 4 is 1/6 because there is 1 favorable outcome out of 6 equally likely outcomes. - 2
Maya flips a fair coin 40 times and gets heads 18 times. What is the experimental probability of getting heads?
The experimental probability of getting heads is 18/40, which simplifies to 9/20 or 45%. - 3
A spinner has 4 equal sections: red, blue, green, and yellow. What is the theoretical probability of landing on green?
Count the number of green sections and divide by the total number of equal sections.
The theoretical probability of landing on green is 1/4 because 1 of the 4 equal sections is green. - 4
A bag contains 3 red marbles, 2 blue marbles, and 5 yellow marbles. What is the theoretical probability of picking a blue marble without looking?
The theoretical probability of picking a blue marble is 2/10, which simplifies to 1/5, because there are 2 blue marbles out of 10 total marbles. - 5
A student rolls a fair number cube 60 times and rolls a 6 exactly 8 times. What is the experimental probability of rolling a 6?
Experimental probability is the number of times the event happened divided by the total number of trials.
The experimental probability of rolling a 6 is 8/60, which simplifies to 2/15. - 6
For a fair number cube, the theoretical probability of rolling an even number is 3/6, or 1/2. If Jamal rolls the cube 20 times, should he always get exactly 10 even numbers? Explain.
Think about whether real results are always perfect matches to predictions.
No, Jamal should not always get exactly 10 even numbers. The theoretical probability predicts what is expected over many trials, but experimental results can vary. - 7
A spinner has 10 equal sections. There are 4 purple sections and 6 orange sections. What is the theoretical probability of landing on purple?
The theoretical probability of landing on purple is 4/10, which simplifies to 2/5 or 40%. - 8
A basketball player makes 12 out of 20 free throws during practice. What is the experimental probability that the player makes a free throw?
Use made shots divided by total shots.
The experimental probability that the player makes a free throw is 12/20, which simplifies to 3/5 or 60%. - 9
A fair coin is flipped once. Find the theoretical probability of tails. Then compare it to an experiment where tails happened 7 times in 10 flips.
The theoretical probability of tails is 1/2, or 50%. The experimental probability is 7/10, or 70%, so the experimental result was higher than the theoretical probability. - 10
A card is chosen from a standard deck of 52 cards. There are 13 hearts in the deck. What is the theoretical probability of choosing a heart?
Divide the number of hearts by the total number of cards.
The theoretical probability of choosing a heart is 13/52, which simplifies to 1/4 or 25%. - 11
The table shows the results of spinning a spinner 50 times: red 14 times, blue 11 times, green 10 times, and yellow 15 times. What is the experimental probability of landing on yellow?
The experimental probability of landing on yellow is 15/50, which simplifies to 3/10 or 30%. - 12
A bag has 1 green tile and 9 white tiles. Without looking, a student picks one tile, replaces it, and repeats this 100 times. About how many times would you expect the student to pick the green tile?
Multiply the probability of green by the number of trials.
The student would expect to pick the green tile about 10 times because the theoretical probability is 1/10 and 1/10 of 100 is 10. - 13
Lena rolls a fair number cube 12 times and gets a 3 five times. The theoretical probability of rolling a 3 is 1/6. Is her experimental probability greater than, less than, or equal to the theoretical probability?
Her experimental probability is 5/12. Since 5/12 is greater than 1/6, her experimental probability is greater than the theoretical probability. - 14
A spinner is divided into 8 equal sections. Three sections are labeled A, two sections are labeled B, and three sections are labeled C. Find the theoretical probability of landing on B.
Use the number of B sections as the favorable outcomes.
The theoretical probability of landing on B is 2/8, which simplifies to 1/4, because 2 of the 8 equal sections are labeled B. - 15
In an experiment, a paper cup lands open side up 22 times out of 50 drops. The theoretical probability is not known. Can you find an experimental probability from the data? Explain.
Experimental probability can be used even when the theoretical probability is hard to know.
Yes, the experimental probability can be found from the data. It is 22/50, which simplifies to 11/25 or 44%, because the cup landed open side up 22 times out of 50 drops.