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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

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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 (a) `0.8750` (b) `0.0875` (c) `0.0625` (d) `0.0250` A. `(1)/(80)` B. `(7)/(80)` C. `(7)/(8)` D. `(1)/(8)` Select the correct answer from above options

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Correct Answer - B Since there are four matches to be played. So, India can get a maximum of 8 points. `therefore` P(Inida gets atleast 7 points) `=P` (Getting exactly 7 points) `+P` (Getting exactly 8 points) `=P` (Getting 2 points in each of the three matches and 1 in one match) `+P` (Getting 2 points in each of the four matches) `=.^4C_(3)(0.5)^3(0.05)^1+.^4C_(4)(0.5)^4` `=4xx(0.5)^3xx(0.05)+(0.5)^4=(0.5)^3(0.2+0.5)=(7)/(80)`

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