Explanation
Solution
Step 1: Understand the Constraints
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Total matches played =2 (vs West Indies) +2 (vs Australia) =4 matches.
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Maximum points possible in 4 matches =4×2=8 points.
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We need the probability of getting at least 7 points, which means the total points can be either 7 or 8.
Step 2: List the Probabilities per Match
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P(0 points)=0.45
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P(1 point)=0.05
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P(2 points)=0.50
Step 3: Identify combinations for at least 7 points
Case 1: Exactly 8 points
This can only happen if India wins all 4 matches (gets 2 points in each).
Case 2: Exactly 7 points
This happens if India gets 2 points in three matches and 1 point in one match.
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Combination: (2,2,2,1) in any order.
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The number of ways to arrange these results is 3!1!4!=4 ways.
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P(7 points)=4×[(0.50)3×(0.05)1]
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P(7 points)=4×[0.125×0.05]
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P(7 points)=4×0.00625=0.0250
Step 4: Calculate Total Probability
P(At least 7)=P(8 points)+P(7 points)
P(At least 7)=0.0625+0.0250
Conclusion:
The probability of India getting at least 7 points is 0.0875.
Correct Option:
(b) 0.0875
