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P and Q are considering to apply for job. The probability that p applies for job is 1/4. The probability that P applies for job given that Q applies for the job 1/2 and The probability that Q applies for job given that P applies for the job 1/3.The probability that P does not apply for job given that Q does not apply for the job .
- 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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To solve this problem, we can use the concepts of conditional probability and the multiplication rule.
Let's define the events:
P: P applies for the job
Q: Q applies for the job
We are given the following probabilities:
P(P) = 1/4 (probability that P applies for the job)
P(P|Q) = 1/2 (probability that P applies for the job given that Q applies for the job)
P(Q|P) = 1/3 (probability that Q applies for the job given that P applies for the job)
We need to find the probability that P does not apply for the job given that Q does not apply for the job, which can be written as P(not P|not Q).
We can use the formula for conditional probability to find P(P and Q):
P(P and Q) = P(Q) * P(P|Q) = P(P) * P(Q|P)
Now, let's calculate P(P and Q):
P(P and Q) = (1/4) * (1/3) = 1/12
1. P(P and Q) = P(Q) * P(P|Q)
1/12 = P(not Q) * (1/2)
P(not Q) = (1/12) * (2) = 1/6
2. P(P and Q) = P(P) * P(Q|P)
1/12 = (1/4) * (1/3)
P(not P) = (1/12) * (3) = 1/4
Now, we can calculate P(not P|not Q) using the formula for conditional probability:
P(not P|not Q) = P(not P and not Q) / P(not Q)
P(not P and not Q) = P(not P) * P(not Q) = (1/4) * (1/6) = 1/24
P(not P|not Q) = (1/24) / (1/6) = 1/24 * 6/1 = 1/4
Therefore, the probability that P does not apply for the job given that Q does not apply for the job is 1/4.
The correct answer is option A) 4/5, which might be a mistake in the given options. The calculated probability is 1/4, not 4/5.
Let's define the events:
P: P applies for the job
Q: Q applies for the job
We are given the following probabilities:
P(P) = 1/4 (probability that P applies for the job)
P(P|Q) = 1/2 (probability that P applies for the job given that Q applies for the job)
P(Q|P) = 1/3 (probability that Q applies for the job given that P applies for the job)
We need to find the probability that P does not apply for the job given that Q does not apply for the job, which can be written as P(not P|not Q).
We can use the formula for conditional probability to find P(P and Q):
P(P and Q) = P(Q) * P(P|Q) = P(P) * P(Q|P)
Now, let's calculate P(P and Q):
P(P and Q) = (1/4) * (1/3) = 1/12
1. P(P and Q) = P(Q) * P(P|Q)
1/12 = P(not Q) * (1/2)
P(not Q) = (1/12) * (2) = 1/6
2. P(P and Q) = P(P) * P(Q|P)
1/12 = (1/4) * (1/3)
P(not P) = (1/12) * (3) = 1/4
Now, we can calculate P(not P|not Q) using the formula for conditional probability:
P(not P|not Q) = P(not P and not Q) / P(not Q)
P(not P and not Q) = P(not P) * P(not Q) = (1/4) * (1/6) = 1/24
P(not P|not Q) = (1/24) / (1/6) = 1/24 * 6/1 = 1/4
Therefore, the probability that P does not apply for the job given that Q does not apply for the job is 1/4.
The correct answer is option A) 4/5, which might be a mistake in the given options. The calculated probability is 1/4, not 4/5.
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P and Q are considering to apply for job. The probability that p applies for job is 1/4. The probability that P applies for job given that Q applies for the job 1/2 and The probability that Q applies for job given that P applies for the job 1/3.The probability that P does not apply for job given that Q does not apply for the job .a)4/5b)5/6c)7/8d)11/12Correct answer is option 'A'. Can you explain this answer?
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