Question

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points $1,2,3$ are $0.45,0.05$ and $0.50$ respectively. Assuming that outcomes are independent, the probability of India getting at least $7$ points is

• A. $0.0624$
• B. $0.0875$
• C. $0.8750$
• D. $0.0250$

Answer 1

The correct option is B $0.0875$

India play $4$ matches and getting at least $7$ points. It can only be possible in $WWWD$ or $WWWW$ position where $W$ represent two points and $D$ represents one point.

$\therefore$ the probability of the required event

${}^4{C}_3\left(0.05\right){\left(0.5\right)}^3{+}^4{C}_4{\left(0.5\right)}^4$

$=\left[{}^4{C}_3\left(0.05\right){+}^4{C}_4\left(0.5\right)\right]{\left(0.5\right)}^3$

$=[\frac{4!}{3!}\left(0.05\right)+0.5]0.125$

$=[4\left(0.05\right)+0.5]0.125$

$=[0.2+0.5]0.125$

$=\left[0.7\right]0.125$

$=0.0875‬$