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:

• A. 0.76
• B. 0.67
• C. 0.78
• D. 0.87

Hint:

A probability tree diagram is an excellent way to visualize these problems. Multiply along the branches and add the results of the successful outcomes.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We use the Theorem of Total Probability. Let \( W \) be the event that the team wins, \( A \) be the event that A is captain, and \( B \) be the event that B is captain.
Step 2: Key Formula or Approach:
\[ P(W) = P(A) \cdot P(W|A) + P(B) \cdot P(W|B) \]
Step 3: Detailed Explanation:
Given:
\( P(A) = 0.6 \)
\( P(B) = 0.4 \)
\( P(W|A) = 0.8 \)
\( P(W|B) = 0.7 \)
Substituting the values:
\[ P(W) = (0.6)(0.8) + (0.4)(0.7) \]
\[ P(W) = 0.48 + 0.28 = 0.76 \]
Step 4: Final Answer:
The total probability of the team winning is 0.76.