Question:
In a cricket team A and B can be chosen as captain, probability of A to be chosen as captain is 0.6, and that of B is 0.4. If A is chosen as captain then probability of winning is 0.8 and if B is chosen then it is 0.7. Then total probability of winning of the team is:
In a cricket team A and B can be chosen as captain, probability of A to be chosen as captain is 0.6, and that of B is 0.4. If A is chosen as captain then probability of winning is 0.8 and if B is chosen then it is 0.7. Then total probability of winning of the team is:
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A probability tree diagram is an excellent way to visualize these problems. Multiply along the branches and add the results of the successful outcomes.
Updated On: Apr 7, 2026
- 0.76
- 0.67
- 0.78
- 0.87
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
This problem uses the Theorem of Total Probability. The event of "winning" depends on which captain is chosen. We sum the probabilities of winning under each specific captain, weighted by the probability of that captain being selected.
Step 2: Key Formula or Approach:
\( P(W) = P(A) \cdot P(W|A) + P(B) \cdot P(W|B) \)
Step 3: Detailed Explanation:
1. Given: - \( P(A) = 0.6 \) (Probability A is captain) - \( P(B) = 0.4 \) (Probability B is captain) - \( P(W|A) = 0.8 \) (Probability of winning given A is captain) - \( P(W|B) = 0.7 \) (Probability of winning given B is captain) 2. Total Probability of winning: \[ P(W) = (0.6 \times 0.8) + (0.4 \times 0.7) \] \[ P(W) = 0.48 + 0.28 = 0.76 \]
Step 4: Final Answer:
The total probability of winning is 0.76.
This problem uses the Theorem of Total Probability. The event of "winning" depends on which captain is chosen. We sum the probabilities of winning under each specific captain, weighted by the probability of that captain being selected.
Step 2: Key Formula or Approach:
\( P(W) = P(A) \cdot P(W|A) + P(B) \cdot P(W|B) \)
Step 3: Detailed Explanation:
1. Given: - \( P(A) = 0.6 \) (Probability A is captain) - \( P(B) = 0.4 \) (Probability B is captain) - \( P(W|A) = 0.8 \) (Probability of winning given A is captain) - \( P(W|B) = 0.7 \) (Probability of winning given B is captain) 2. Total Probability of winning: \[ P(W) = (0.6 \times 0.8) + (0.4 \times 0.7) \] \[ P(W) = 0.48 + 0.28 = 0.76 \]
Step 4: Final Answer:
The total probability of winning is 0.76.
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