Mark the correct alternative in each of the following:
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
India wins = W = 2 pt
India loses = L = 0 pt
India draws = D = 1 pt
Total matches played by India = 4
This means that the total points needs to be 7 at least
Either India wins all 4 matches or India wins 3 and draws 1
the probability of WWWW = (0.5)*(0.5)*(0.5)*(0.5) = 0.0625
India wins 3 matches and draws 1: probability in that case = (0.5)*(0.5)*(0.5)*(0.05) = 0.00625
The 4 possible outcomes will be:
WWWD, WWDW, WDWW, DWWW
Total probability of India wins 3 matches and draws 1 = 4*(0.00625) = 0.025
P( total points have to be at least 7) = 0.0625 + 0.025 = 0.0875