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A student appear for tests I,II and III.The student is
successful if he passes either in tests I and II or
tests I and III.The probabilities of the student passing
in tests I,II and III are p,q and 1/2 respectively. If the
probability that the student is successful is 1/2, then
- a)p = q = 1
- b)p = q = 1/2
- c)p = 1, q = 0
- d)p = 1, q = 1/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A student appear for tests I,II and III.The student issuccessful if he...
Solution:
To find the probabilities of passing in tests I and II, and tests I and III, we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
Let's calculate the probabilities:
P(passing in tests I and II) = P(A) = p
P(passing in tests I and III) = P(B) = 1/2
We also know that the probability of the student being successful is 1/2. Therefore,
P(successful) = P(A or B) = 1/2
Using the formula, we can substitute the values and solve for P(A and B):
1/2 = p + 1/2 - P(A and B)
1/2 - p = - P(A and B)
P(A and B) = p - 1/2
Now, let's consider the possible combinations of passing the tests:
1. Passing in tests I and II:
P(A) = p
2. Passing in tests I and III:
P(B) = 1/2
3. Passing in tests II and III:
P(A and B) = p - 1/2
4. Passing in all three tests:
P(A and B and C) = p * q * 1/2
Since the student is successful if they pass either in tests I and II or tests I and III, we can write the probability of being successful as:
P(successful) = P(A and B) + P(B and C) - P(A and B and C)
Substituting the values, we get:
1/2 = p + 1/2 - p + 1/2 - p * q * 1/2
Simplifying the equation, we have:
1/2 = 1 - p * q * 1/2
Multiplying both sides by 2, we get:
1 = 2 - p * q
Rearranging the equation, we have:
p * q = 1
Since p and q represent probabilities, they must be between 0 and 1. Therefore, the only possible values for p and q are:
p = 1, q = 1
Therefore, the correct answer is option C: p = 1, q = 0.
To find the probabilities of passing in tests I and II, and tests I and III, we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
Let's calculate the probabilities:
P(passing in tests I and II) = P(A) = p
P(passing in tests I and III) = P(B) = 1/2
We also know that the probability of the student being successful is 1/2. Therefore,
P(successful) = P(A or B) = 1/2
Using the formula, we can substitute the values and solve for P(A and B):
1/2 = p + 1/2 - P(A and B)
1/2 - p = - P(A and B)
P(A and B) = p - 1/2
Now, let's consider the possible combinations of passing the tests:
1. Passing in tests I and II:
P(A) = p
2. Passing in tests I and III:
P(B) = 1/2
3. Passing in tests II and III:
P(A and B) = p - 1/2
4. Passing in all three tests:
P(A and B and C) = p * q * 1/2
Since the student is successful if they pass either in tests I and II or tests I and III, we can write the probability of being successful as:
P(successful) = P(A and B) + P(B and C) - P(A and B and C)
Substituting the values, we get:
1/2 = p + 1/2 - p + 1/2 - p * q * 1/2
Simplifying the equation, we have:
1/2 = 1 - p * q * 1/2
Multiplying both sides by 2, we get:
1 = 2 - p * q
Rearranging the equation, we have:
p * q = 1
Since p and q represent probabilities, they must be between 0 and 1. Therefore, the only possible values for p and q are:
p = 1, q = 1
Therefore, the correct answer is option C: p = 1, q = 0.
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A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer?
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A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer?.
A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer?.
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A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A student appear for tests I,II and III.The student issuccessful if he passes either in tests I and II ortests I and III.The probabilities of the student passingin tests I,II and III are p,q and 1/2 respectively. If theprobability that the student is successful is 1/2, thena)p = q = 1b)p = q = 1/2c)p = 1, q = 0d)p = 1, q = 1/2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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