Question

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points $0,1$ and $2$ 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. 0.8750
• B. 0.0875
• C. 0.0625
• D. 0.0250

Answer 1

Answer: (B)

India play $4$ matches and getting at least $7$ points. It can only be possible in $WWWD$ or $WWWW$ position, where $W$ represents two points and $D$ represents one point.
Therefore, the probability of the required event
$={}^4{C}_3(0.05)(0.5{)}^3+{}^4{C}_4(0.5{)}^4$
$=[4(0.05)+0.5](0.5{)}^3=0.0875$