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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 in the third test, is
(Round off up to 2 decimal places)
Correct answer is '0.25'. Can you explain this answer?
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The probability of India winning a test match against West Indies is ...
Given: P(India wins) = p = 1/2
P(India loses) = p' = 1/2
Out of 5 matches, India's second win occurs in the third test.
⇒ India wins the third test and simultaneously it has won one match from the first two and lost the other.
Required probability = P(LWW) + P(WLW)
= 
= 0.25
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The probability of India winning a test match against West Indies is ...
Probability of India winning a test match against West Indies:
The probability of India winning a test match against West Indies is given as 1/2. This means that out of every two test matches between India and West Indies, India is expected to win one and lose one.
Probability of India's second win occurring in the third test:
To calculate the probability that India's second win occurs in the third test, we need to consider the possible outcomes in a 5-match series.
Possible outcomes in a 5-match series:
In a 5-match series, India can win the second match in any of the following ways:
- India wins the first match and then wins the second match.
- India loses the first match, wins the second match, and then wins the third match.
- India loses the first two matches, wins the third match, and then wins the fourth and fifth matches.
Calculating the probability:
To calculate the probability, we need to find the probability of each of these outcomes and add them up.
Probability of India winning the first match:
The probability of India winning the first match is 1/2.
Probability of India winning the second match given that they won the first match:
Since the outcome of each match is independent, the probability of India winning the second match, given that they won the first match, is also 1/2.
Probability of India losing the first match and winning the second match:
The probability of India losing the first match is also 1/2. The probability of winning the second match, given that they lost the first match, is again 1/2.
Probability of India losing the first two matches and winning the third match:
The probability of India losing the first two matches is (1/2)*(1/2) = 1/4. The probability of winning the third match, given that they lost the first two matches, is again 1/2.
Calculating the total probability:
Now, we can calculate the total probability by adding up the probabilities of each outcome:
(1/2)*(1/2) + (1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2)*(1/2) = 1/4 + 1/8 + 1/16 = 4/16 + 2/16 + 1/16 = 7/16
Therefore, the probability that India's second win occurs in the third test is 7/16.
The probability of India winning a test match against West Indies is given as 1/2. This means that out of every two test matches between India and West Indies, India is expected to win one and lose one.
Probability of India's second win occurring in the third test:
To calculate the probability that India's second win occurs in the third test, we need to consider the possible outcomes in a 5-match series.
Possible outcomes in a 5-match series:
In a 5-match series, India can win the second match in any of the following ways:
- India wins the first match and then wins the second match.
- India loses the first match, wins the second match, and then wins the third match.
- India loses the first two matches, wins the third match, and then wins the fourth and fifth matches.
Calculating the probability:
To calculate the probability, we need to find the probability of each of these outcomes and add them up.
Probability of India winning the first match:
The probability of India winning the first match is 1/2.
Probability of India winning the second match given that they won the first match:
Since the outcome of each match is independent, the probability of India winning the second match, given that they won the first match, is also 1/2.
Probability of India losing the first match and winning the second match:
The probability of India losing the first match is also 1/2. The probability of winning the second match, given that they lost the first match, is again 1/2.
Probability of India losing the first two matches and winning the third match:
The probability of India losing the first two matches is (1/2)*(1/2) = 1/4. The probability of winning the third match, given that they lost the first two matches, is again 1/2.
Calculating the total probability:
Now, we can calculate the total probability by adding up the probabilities of each outcome:
(1/2)*(1/2) + (1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2)*(1/2) = 1/4 + 1/8 + 1/16 = 4/16 + 2/16 + 1/16 = 7/16
Therefore, the probability that India's second win occurs in the third test is 7/16.
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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 in the third test, is(Round off up to 2 decimal places)Correct answer is '0.25'. Can you explain this answer?
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