India play two matches each with West Indies and Australia. In any match the probabilities of India getting 0,1 and 2 points 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. 0875` b. `1//16` c. `0. 1125` d. none of these

Options

A. `(1)/(80)`
B. `(7)/(80)`
C. `(7)/(8)`
D. `(1)/(8)`

Answer

B

Explanation

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)`