Question

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points $0,1,2$ are $0.45,0.05,0.50$ 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. $0.0250$

Answer 1

The correct option is B $0.0875$

Since there are just four matches to be played India can get a maximum of $8$ points.
$\therefore P($ India gets at least $7$ points $)=P($ getting exactly $7$ points$)+P($ getting exactly $8$ points $)$
$=P($ getting $2$ in each of the $3$ matches and $1$ in one match $)+P($getting $2$ in each of the four matches$)$
${=}^4{C}_3{\left(0.5\right)}^3\left(0.05\right){+}^4{C}_4{\left(0.5\right)}^4=0.025+0.0625=0.0875$