Q. 54.5( 2 Votes )

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

A. 0.0875

B. 1/16

C. 0.1125

D. none of these

Answer :

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

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