Six friends decide to share a big cake. Since all of them like the cake, they…
2024
Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums to a number between 2 and 12. Which total would be likely to appear more often 8,9 or 10?
- A.
8
- B.
9
- C.
10
- D.
All are equally likely
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Show answer & explanation
Correct answer: A
Key insight: Picking a card (1–6) and rolling a die (1–6) produce 36 equally likely ordered pairs (card, die). Count how many ordered pairs give each sum.
Counts and probabilities for each relevant total:
Total 8: ordered pairs (2,6), (3,5), (4,4), (5,3), (6,2) — 5 outcomes, probability 5/36 (≈13.9%).
Total 9: ordered pairs (3,6), (4,5), (5,4), (6,3) — 4 outcomes, probability 4/36 (≈11.1%).
Total 10: ordered pairs (4,6), (5,5), (6,4) — 3 outcomes, probability 3/36 (≈8.3%).
For reference: total 7 has 6 outcomes ((1,6),(2,5),(3,4),(4,3),(5,2),(6,1)), the single most likely sum, but 7 is not one of the answer choices.
Conclusion: Among the given choices, the total 8 is most likely because it has the largest number of ordered pairs (5) that produce it, so 8 will appear more often than 9 or 10.