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:
Answer & explanation
Correct answer: option 1
The correct answer is option 1: 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
The total probability of at least 7 points = 0.025 + 0.0625 = 0.0875