Experimental vs Theoretical

Question 1

A bag contains 5 red, 5 blue, and 5 green marbles (so each colour has a 1/3 chance). Maya draws a marble, notes its colour, puts it back, and repeats this 60 times. She gets 22 red, 18 blue and 20 green. If she repeats the same experiment 600 times, which statement best describes what is most likely to happen?

Accepted Answer

The numbers for each colour will be closer to 200, so the percentages will be nearer to 33 % for each colour.

Answer

She will get exactly 200 of each colour because the theoretical probability guarantees it.

Answer

She will get the same counts as in the 60‑draw experiment (22 red, 18 blue, 20 green).

Answer

Because more trials give more room for randomness, the counts could be even farther from 200 for each colour.

Question 2

Lila draws one card from a standard 52‑card deck, records whether it is a heart, puts the card back, and repeats this 25 times. The theoretical probability of drawing a heart each time is 13/52 = 1/4, so she expects about 6 hearts. She actually gets only 2 hearts. Which statement best explains why her result is lower than expected and what would happen if she performed the experiment 250 times instead of 25?

Accepted Answer

Because each draw is random, a small number of trials can give a result far from the expected 1/4; with many more draws the proportion of hearts will most likely move closer to 1/4.

Answer

Because the deck does not have enough hearts, adding more draws will not change the proportion of hearts she gets.

Answer

Because she replaced the cards after each draw, the probability of a heart actually gets smaller each time, so more draws would make the proportion even lower.

Answer

Because she probably counted the hearts incorrectly; a correct count would match the theoretical probability exactly, no matter how many draws.

Question 3

A student rolls a fair six‑sided die 60 times and records that the number 3 appears 8 times instead of the expected 10 times. Which statement best explains why her experimental result isn’t exactly the same as the theoretical prediction, but would become closer if she rolled the die many more times?

Accepted Answer

Each roll is random, so with only a few rolls the counts can be a little higher or lower; with many rolls the average count gets nearer the expected value.

Answer

The die must be weighted, so it can never match the theoretical number no matter how many rolls are made.

Answer

She probably missed counting some rolls, so the numbers are off.

Answer

The probability of getting a 3 changes after each roll, making the result different each time.

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