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14.Probability
hard
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0, 1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is
A
$0.8750$
B
$0.0875$
C
$0.0625$
D
$0.0250$
(IIT-1992)
Solution
(b) Matches played by India are four. Maximum points in any match are $2$.
$\therefore $ Maximum points in four matches can be $8$ only.
Therefore probability $(P) = p(7) + p(8)$
$p(7) = {}^4{C_1}(0.05){(0.5)^3} = 0.0250$
$p(8) = {(0.5)^4} = 0.0625$
$ \Rightarrow P = 0.0875$.
Standard 11
Mathematics
