Final answer:
The correct answer is option B. To find the probability of India scoring at least 7 points in four matches, we consider the different outcomes and multiply the probabilities due to the independence of events, resulting in a probability of 0.0875 (Option B).
Step-by-step explanation:
The question deals with calculating the probability of India scoring at least 7 points from two matches each with West Indies and Australia. With the probabilities of 0, 1, and 2 points being 0.45, 0.05, and 0.50 respectively, and assuming independence of matches, we want to find the probability of India scoring at least 7 points in these four matches. We can calculate this by considering the outcomes where India scores the required points - for example, winning all four matches (2 points each), or winning three and drawing one (1 point), and so on. To calculate the probability of each outcome, we multiply the probabilities of the individual match results because they are independent events. Afterwards, adding up these probabilities gives us the total probability of India scoring at least 7 points.
When we calculate each scenario's probability, we find that the only possibilities for India to score at least 7 points are by scoring 2 points in three matches and 1 point in one match, or by scoring 2 points in all four matches. By multiplying the probabilities of each independent event and then summing the probabilities for all scenarios, we can find the correct answer. The correct option that represents the probability of India getting at least 7 points is: