India play 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

The correct answer is: 0.0875

Probability of getting at least seven points = Probability of getting 7 points or 8 points = probability of getting 7 points + probability of getting 8 points.
Seven points in four matches can be obtained in the following four different ways:
(2, 2, 2, 1) ; (2, 2, 1, 2); (2, 1, 2, 2); (1, 2, 2, 2)
Hence probability of getting 7 points = 4. (0.50)³ (0.05) = 0.0250
Eight points in four matches can be obtained only in one way i.e. 2, 2, 2, 2, Hence probability of getting 8 points = (0.50)⁴ = 0.0625
Thus the required probability = 0.0250 + 0.0625 = 0.0875.