India play four matches 2 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. Assume that the outcomes are independent, the probability of India getting at least 7 points is:

0.0875

4 matches

7 points → 2 + 2 + 2 + 1 (only possible case)

Favourable no. of ways to get 7 points = different no. of arrangements of three 2’s and one $1 = \frac{4!}{3!}=4$

For each arrangement (lets say 2, 1, 2, 2)

Probability of getting that arrangement = 4 × (0.5 × 0.5 × 0.5 × 0.05) = 0.025

8 point → 2 + 2 + 2 + 2

Probability of getting 8 points = (0.5)⁴ = 0.0625

Total probability = 0.025 = 0.0625 = 0.0875