Question

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

• A. $0.0875$
• B. $\frac{1}{16}$
• C. $0.1125$
• D. none of these

Answer 1

The correct option is A $0.0875$

India plays total $4$ matches.
$P\left(getting0\right)=0.45P\left(getting1\right)=0.05P\left(getting2\right)=0.5$
at least $7$ points can be obtained in following ways:
$(2,2,2,1),(2,2,2,2)$
Let the event of obtaining at least $7$ points be $E$ then
$P\left(E\right)=\left({}^4{C}_1\right)P\left(2\right)P\left(2\right)P\left(2\right)P\left(1\right)+P\left(2\right)P\left(2\right)P\left(2\right)P\left(2\right)=4\times {0.5}^3\times 0.05+{0.5}^4=0.0875$