Question:
Three players A, B and C play a game. The probability that A, B and C finish the game are respectively \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \). The probability that the game is finished is
Three players A, B and C play a game. The probability that A, B and C finish the game are respectively \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \). The probability that the game is finished is
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“At least one” problems are easiest using complement probability.
Updated On: May 1, 2026
- \( \frac{1}{8} \)
- \( 1 \)
- \( \frac{1}{4} \)
- \( \frac{3}{4} \)
- \( \frac{1}{2} \)
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The Correct Option is D
Solution and Explanation
Concept:
Probability at least one finishes:
\[
1 - P(\text{none finish})
\]
Step 1: Compute none finish.
\[ (1-\tfrac{1}{2})(1-\tfrac{1}{3})(1-\tfrac{1}{4}) = \tfrac{1}{2}\cdot \tfrac{2}{3}\cdot \tfrac{3}{4} = \tfrac{1}{4} \]
Step 2: Subtract from 1.
\[ 1 - \tfrac{1}{4} = \tfrac{3}{4} \]
Step 1: Compute none finish.
\[ (1-\tfrac{1}{2})(1-\tfrac{1}{3})(1-\tfrac{1}{4}) = \tfrac{1}{2}\cdot \tfrac{2}{3}\cdot \tfrac{3}{4} = \tfrac{1}{4} \]
Step 2: Subtract from 1.
\[ 1 - \tfrac{1}{4} = \tfrac{3}{4} \]
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