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

Options

A. (a) `0.8750`
B. (b) `0.0875`
C. (c) `0.0625`
D. (d) `0.0250`

Answer

(b) `0.0875`

Explanation

Given,

Total no's of matches played by India `= 4`

Maximum point in any two matches `= 2`

`therefore`, The maximum number of points in `4` matches `= 4(2) = 8`


Thus, required probability `= P(7) + P(8)`

`= 4_(C_3) 0.5^3(0.05) + 4_(C_4) 0.5^4`

`= 0.025 + 0.0625`

`= 0.0875`


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