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Question 46

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

Solution

Total matches played = 4

Maximum points = 2 * 4 = 8

So to get atleast 7 points , India needs to win atleast 3 matches and one can be draw.

1. India wins all 4 matches: There is only one possible outcome

Hence, the probability of 4 wins = (0.5)*(0.5)*(0.5)*(0.5) = 0.0625

2. India wins 3 matches and draws 1: probability in that case = (0.5)*(0.5)*(0.5)*(0.05) = 0.00625

Total probability of India wins 3 matches and draws 1 = 4*(0.00625) = 0.025

(since 4 cases, any one match an be draw)

P = 0.0625 + 0.025 = 0.0875

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