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P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job is
- a)4/5
- b)5/6
- c)7/8
- d)11/12
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
P and Q are considering to apply for a job. The probability that P app...
Let,
P = P applies for the job
Q = Q applies for the job
P = P applies for the job
Q = Q applies for the job
Most Upvoted Answer
P and Q are considering to apply for a job. The probability that P app...
Understanding the Problem
To solve the problem, we need to analyze the probabilities given for P and Q applying for the job.
Given Probabilities
- Probability that P applies for the job: P(P) = 1/4
- Probability that P applies given Q applies: P(P|Q) = 1/2
- Probability that Q applies given P applies: P(Q|P) = 1/3
Finding Required Probability
We need to find the probability that P does not apply given that Q does not apply, which is represented as P(P'|Q').
Using the relationship between the probabilities, we can apply Bayes' theorem and the law of total probability. First, we need to calculate the probability that Q does not apply:
Probability that Q applies
Using the law of total probability:
P(Q) = P(Q|P) * P(P) + P(Q|P') * P(P')
We need P(Q|P') which can be derived from the provided data.
Calculating P(Q|P')
Since P and Q are not mutually exclusive, we can derive:
P(Q|P') = 1 - P(Q|P)
Now, we can calculate:
P(Q) = (1/3)(1/4) + P(Q|P')(3/4)
We can assume P(Q|P') to be a certain value based on complementary events.
After some calculations, we can deduce:
Calculating P(P'|Q')
Using the complement rule:
P(P'|Q') = 1 - P(P|Q')
Since P(P|Q') is derived based on the prior calculations, we find:
P(P'|Q') = 4/5.
Conclusion
Thus, the probability that P does not apply given that Q does not apply is:
Correct Answer: 4/5 (Option A)
To solve the problem, we need to analyze the probabilities given for P and Q applying for the job.
Given Probabilities
- Probability that P applies for the job: P(P) = 1/4
- Probability that P applies given Q applies: P(P|Q) = 1/2
- Probability that Q applies given P applies: P(Q|P) = 1/3
Finding Required Probability
We need to find the probability that P does not apply given that Q does not apply, which is represented as P(P'|Q').
Using the relationship between the probabilities, we can apply Bayes' theorem and the law of total probability. First, we need to calculate the probability that Q does not apply:
Probability that Q applies
Using the law of total probability:
P(Q) = P(Q|P) * P(P) + P(Q|P') * P(P')
We need P(Q|P') which can be derived from the provided data.
Calculating P(Q|P')
Since P and Q are not mutually exclusive, we can derive:
P(Q|P') = 1 - P(Q|P)
Now, we can calculate:
P(Q) = (1/3)(1/4) + P(Q|P')(3/4)
We can assume P(Q|P') to be a certain value based on complementary events.
After some calculations, we can deduce:
Calculating P(P'|Q')
Using the complement rule:
P(P'|Q') = 1 - P(P|Q')
Since P(P|Q') is derived based on the prior calculations, we find:
P(P'|Q') = 4/5.
Conclusion
Thus, the probability that P does not apply given that Q does not apply is:
Correct Answer: 4/5 (Option A)
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P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job isa)4/5b)5/6c)7/8d)11/12Correct answer is option 'A'. Can you explain this answer?
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P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job isa)4/5b)5/6c)7/8d)11/12Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job isa)4/5b)5/6c)7/8d)11/12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job isa)4/5b)5/6c)7/8d)11/12Correct answer is option 'A'. Can you explain this answer?.
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