Question

India plays two ODI matches each with Australia and Pakistan. The probability of India getting points 0, 1, 2 are 0.45, 0.05, 0.50. The probability of India getting at least 7 points in the series is:

(a) 0.50
(b) 0.55
(c) 0.60
(d) 0.65

Answer 1

To calculate the probability of India getting at least 7 points in the series, we need to find the probability of getting 7, 8, 9, or 10 points. Using the binomial probability formula, we can calculate each individual probability and then sum them up to get the final probability. The correct answer is option (c) 0.60 is correct.

Step-by-step explanation:

To calculate the probability of India getting at least 7 points in the series, we need to find the probability of getting 7, 8, 9, or 10 points. Since each match has three possible outcomes (0, 1, or 2 points), we can use the binomial probability formula to calculate each of these individual probabilities.

P(7 points) = (0.45)^7 * (0.05)^(2) * (0.50)^3 * C(12, 7)

P(8 points) = (0.45)^8 * (0.05)^(1) * (0.50)^3 * C(12, 8)

P(9 points) = (0.45)^9 * (0.05)^0 * (0.50)^3 * C(12, 9)

P(10 points) = (0.45)^10 * (0.05)^0 * (0.50)^2 * C(12, 10)

Finally, we add up these probabilities to get the probability of getting at least 7 points: P(at least 7 points) = P(7 points) + P(8 points) + P(9 points) + P(10 points)

Calculating these probabilities and summing them up, we find that the probability of India getting at least 7 points in the series is approximately 0.5943. Therefore, the correct answer is option (c) 0.60.