Question

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
  

Answer 1

The correct option is B 0.0875

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)
$P\left(7\right){=}^4{C}_1\left(0.05\right)(0.5{)}^3=0.0250$
$P\left(8\right)=(0.5{)}^4=0.0625$
$\Rightarrow P=0.0875$