India play two matches each with West Indies and Australia. In any mat

1.	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 isA. 0.0875B. 1/16C. 0.1125D. none of these
Answer» Correct option is A.0.0875 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

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 isA. 0.0875B. 1/16C. 0.1125D. none of these

Answer»

Correct option is A.0.0875

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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