Question 11 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
Shawn is playing a game with a set of cards. Half of them are blue and the other half are yellow. In the game, the player guesses the color of the top card, looks at the card, and returns the card to the deck. The player continues to do this, shuffling the deck after each guess.
Answer
A
Yes, Shawn has guessed well so far, so it is clear that he cannot miss.
B
No, all of the cards have been blue so far, so the next one must also be blue.
C
Yes, half of the cards are yellow, so the fourth card should be yellow to compensate for the first three cards being blue.
D
No, the law of large numbers says that the proportion of yellow cards should approach the true probability after many trials.
Explanation
Because Shawn returns and shuffles each card, each guess is an independent trial. The chance that the next card is yellow remains 1/2, even if the first three cards were blue; the deck does not need to “compensate” on the fourth draw. Over many trials, the proportion of yellow cards is expected to get closer to 1/2, which is the law of large numbers. Choice D gives this explanation.
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