The sweets jar puzzle
✓ With solution
Sweets in three colours, and the room is dark. How many should you take, and what are your chances?
A jar holds 10 sweets that look and feel exactly the same: 5 red, 3 green and 2 yellow. The power has gone out and you can't see the colours.
What is the smallest number of sweets you must take to be sure you have 2 green ones?
- A2
- B4
- C7
- D9
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Answer: D) 9. Think of the worst luck: you might take all 5 red first, then both yellow, which is 7 sweets and not one green. After that only green ones are left, so you need 2 more: 7 + 2 = 9. With fewer than 9 you could end up with only one green, or none.
You put all the sweets back, then take 2 at random.
What is the chance that both are green?
- A1 in 15
- B9 in 100
- C1 in 5
- D3 in 10
Show the answer
Answer: A) 1 in 15. The chance the first sweet is green is 3 in 10. Then 9 sweets are left, 2 of them green, so the chance the second is green too is 2 in 9. Multiply them: 3/10 × 2/9 = 6/90, which is 1 in 15. (9 in 100 would only be right if you put the first sweet back before taking the second.)
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