Question:
In a chess tournament, assume that your probability of winning a game is 0.3 against level 1 players, 0.4 against level 2 players and 0.5 against level 3 players. If among the players 50% are level 1, 25% are level 2 and the remaining are level 3, the probability of winning a game against a randomly chosen player is
In a chess tournament, assume that your probability of winning a game is 0.3 against level 1 players, 0.4 against level 2 players and 0.5 against level 3 players. If among the players 50% are level 1, 25% are level 2 and the remaining are level 3, the probability of winning a game against a randomly chosen player is
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Weighted averages = probability × proportion.
Updated On: Apr 30, 2026
- $0.275$
- $0.375$
- $0.225$
- $0.325$
- $0.125$
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The Correct Option is A
Solution and Explanation
Concept: Total Probability Theorem
Step 1: Given probabilities \[ P(L_1)=0.5, P(L_2)=0.25, P(L_3)=0.25 \] \[ P(W|L_1)=0.3, P(W|L_2)=0.4, P(W|L_3)=0.5 \]
Step 2: Apply total probability \[ P(W) = \sum P(L_i)P(W|L_i) \] \[ = (0.5)(0.3) + (0.25)(0.4) + (0.25)(0.5) \]
Step 3: Compute \[ = 0.15 + 0.10 + 0.125 = 0.375 \] \[ \boxed{0.375} \]
Step 1: Given probabilities \[ P(L_1)=0.5, P(L_2)=0.25, P(L_3)=0.25 \] \[ P(W|L_1)=0.3, P(W|L_2)=0.4, P(W|L_3)=0.5 \]
Step 2: Apply total probability \[ P(W) = \sum P(L_i)P(W|L_i) \] \[ = (0.5)(0.3) + (0.25)(0.4) + (0.25)(0.5) \]
Step 3: Compute \[ = 0.15 + 0.10 + 0.125 = 0.375 \] \[ \boxed{0.375} \]
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