Question

Ms. Kingsley creates a game for a school festival. In her game, students draw a lettered token from the bag. Students win a prize depending on which letter is on the drawn token. Then the token is returned to the bag. The table below shows the three possible outcomes and the count of each type of token in the bag.



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Marcie, a student at the school, keeps track of the results of 20 consecutive draws from the bag before she plays the game. She records these results in a table, as shown below.



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Which statements about the game are true? Choose ALL that are correct.


From Marcie's observed frequencies, the probability of winning a small prize is 0.250.


The theoretical probability of winning a small prize is 0.100.


The more observations that are recorded, the closer the observed probability model will be to the theoretical probability model.


The theoretical probability of winning a large prize is 0.125.


From Marcie's observed frequencies, the probability of not winning is 0.650.


The observed probability model matches the theoretical probability model.

Answer 1

True: statements 1, 2, 3, 4, 5. False: statement 6.

Work:
- Marcie observed 20 draws: small = 5, large = 2, no prize = 13 → observed probabilities 5/20 = 0.25, 2/20 = 0.10, 13/20 = 0.65. So (1) and (5) are true.
- The bag has 40 tokens (5 large, 4 small, 31 no prize), so theoretical probabilities are small = 4/40 = 0.100 and large = 5/40 = 0.125, so (2) and (4) are true.
- (3) is true by the Law of Large Numbers: with more observations the observed model tends to get closer to the theoretical model.
- The observed probabilities (0.25, 0.10, 0.65) do not match the theoretical probabilities (0.10, 0.125, 0.775), so (6) is false.