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The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)
- a)1/8
- b)1/4
- c)1/2
- d)2/3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The probability of India winning a test match against west Indies is 1...
Given that P (India wins) = p = 1/2
∴ P (India loses) = p' = 1/2 Out of 5 matches india’s second win occurs at third test
⇒ India wins third test and simultaneously it has won one match from first two and lost the other.
∴ Required prob. = P (LWW) + P (WLW)
∴ P (India loses) = p' = 1/2 Out of 5 matches india’s second win occurs at third test
⇒ India wins third test and simultaneously it has won one match from first two and lost the other.
∴ Required prob. = P (LWW) + P (WLW)
Most Upvoted Answer
The probability of India winning a test match against west Indies is 1...
Wins at least 3 matches can be calculated using the binomial distribution.
The binomial distribution calculates the probability of getting a certain number of successes (India winning a match) in a fixed number of independent Bernoulli trials (5 matches).
To find the probability that India wins at least 3 matches in a 5-match series, we need to calculate the probabilities of winning 3, 4, and 5 matches and then sum them up.
P(India wins at least 3 matches) = P(India wins 3 matches) + P(India wins 4 matches) + P(India wins 5 matches)
P(India wins k matches) = (5Ck) * (1/2)^k * (1/2)^(5-k)
Where (5Ck) is the binomial coefficient that represents the number of ways to choose k successes from 5 trials.
Calculating each term separately:
P(India wins 3 matches) = (5C3) * (1/2)^3 * (1/2)^(5-3) = 10 * (1/8) * (1/8) = 10/64 = 5/32
P(India wins 4 matches) = (5C4) * (1/2)^4 * (1/2)^(5-4) = 5 * (1/16) * (1/2) = 5/32
P(India wins 5 matches) = (5C5) * (1/2)^5 * (1/2)^(5-5) = 1 * (1/32) * (1/1) = 1/32
Now, summing up the probabilities:
P(India wins at least 3 matches) = 5/32 + 5/32 + 1/32 = 11/32
Therefore, the probability that India wins at least 3 matches in a 5-match series against West Indies is 11/32.
The binomial distribution calculates the probability of getting a certain number of successes (India winning a match) in a fixed number of independent Bernoulli trials (5 matches).
To find the probability that India wins at least 3 matches in a 5-match series, we need to calculate the probabilities of winning 3, 4, and 5 matches and then sum them up.
P(India wins at least 3 matches) = P(India wins 3 matches) + P(India wins 4 matches) + P(India wins 5 matches)
P(India wins k matches) = (5Ck) * (1/2)^k * (1/2)^(5-k)
Where (5Ck) is the binomial coefficient that represents the number of ways to choose k successes from 5 trials.
Calculating each term separately:
P(India wins 3 matches) = (5C3) * (1/2)^3 * (1/2)^(5-3) = 10 * (1/8) * (1/8) = 10/64 = 5/32
P(India wins 4 matches) = (5C4) * (1/2)^4 * (1/2)^(5-4) = 5 * (1/16) * (1/2) = 5/32
P(India wins 5 matches) = (5C5) * (1/2)^5 * (1/2)^(5-5) = 1 * (1/32) * (1/1) = 1/32
Now, summing up the probabilities:
P(India wins at least 3 matches) = 5/32 + 5/32 + 1/32 = 11/32
Therefore, the probability that India wins at least 3 matches in a 5-match series against West Indies is 11/32.
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The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer?
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The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer?.
The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability of India winning a test match against west Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at third test is (1995S)a)1/8b)1/4c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer?.
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