India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is
- 0.0624
- 0.0875
- 0.8750
- 0.0250
The Correct Option is B
Solution and Explanation
Total matches played = 4
Maximum points = \(2 \times 4 = 8\)
So, to get at least 7 points, India needs to win at least 3 matches and one can be draw.
India wins all 4 matches: There is only one possible outcome
Hence, the probability of 4 wins = \((0.5)\times(0.5)\times(0.5)\times(0.5) = 0.0625\)
India wins 3 matches and draws 1: probability in that case = \((0.5)\times(0.5)\times(0.5)\times(0.05) = 0.00625\)
Total probability of India wins 3 matches and draws 1 = \(4\times(0.00625) = 0.025\)
(since 4 cases, any one match can be draw)
\(P = 0.0625 + 0.025 = 0.0875\)
The correct option is (B): 0.0875
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