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. 0.0624
• B. 0.0875
• C. 0.8750
• D. 0.0250

Answer 1

Answer: (B)

0.0875

Answer 2

Total matches played = 4
Maximum points = $2 \times 4 = 8$

So, to get at least 7 points, India needs to win at least 3 matches and one can be draw.
India wins all 4 matches: There is only one possible outcome

Hence, the probability of 4 wins = $(0.5)\times(0.5)\times(0.5)\times(0.5) = 0.0625$
India wins 3 matches and draws 1: probability in that case = $(0.5)\times(0.5)\times(0.5)\times(0.05) = 0.00625$

Total probability of India wins 3 matches and draws 1 = $4\times(0.00625) = 0.025$
(since 4 cases, any one match can be draw)
$P = 0.0625 + 0.025 = 0.0875$

The correct option is (B): 0.0875