A box contains 16 red, 12 white, and 15 yellow identical marbles. A man picks one marble at a time without replacement. How many times must he pick a marble to be 100% certain of picking at least 3 white marbles?
A box contains 16 red, 12 white, and 15 yellow identical marbles. A man picks one marble at a time without replacement. How many times must he pick a marble to be 100% certain of picking at least 3 white marbles?
Show Hint
- 33
- 34
- 31
- 32
The Correct Option is B
Solution and Explanation
Concept: Worst-case selection (pigeonhole principle).
Explanation: To ensure 3 white marbles, assume the worst case: pick all non-white first. Non-white marbles: \[ 16 + 15 = 31 \] After picking 31 marbles, there are still 0 white marbles in the worst case. Now pick whites: To guarantee 3 whites: \[ 31 + 3 = 34 \]
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