Question 1200597: Untitled
Feb 24, 2023
6. An engineering Company advertises a job in three news papers A,B,C.if it is
known that these papers attract undergraduate engineering readerships in the
proportions 2:3:1. The probabiity that an engineerig undergraduate sees and
replies to the Job advertisement in the papers are 0.002, 0.001 and 0.005
respectively. Assume that the ungergraduate sees Only one job advertisement a)
the ergineering company receives only one reply to it advertisements, calculate
the probability that the applicant has seen the job adv ertised in place.
1.a,A b,B, c,C.
2.if the company recaives two replies, what is the probability that both
applicants saw the jOb advertised in paper A?
Answer by GingerAle(43)   (Show Source):
You can put this solution on YOUR website! Certainly, let's calculate the probabilities.
**1. Probability that the applicant has seen the job advertised in paper A, given only one reply:**
* **Define Probabilities:**
* Let P(A), P(B), and P(C) be the probabilities of an undergraduate seeing the ad in papers A, B, and C, respectively.
* Let R(A), R(B), and R(C) be the probabilities of replying to the ad in papers A, B, and C, respectively.
* **Given:**
* P(A) = 2/6 = 1/3
* P(B) = 3/6 = 1/2
* P(C) = 1/6
* R(A) = 0.002
* R(B) = 0.001
* R(C) = 0.005
* **Calculate the probability of receiving a reply from each paper:**
* P(reply from A) = P(A) * R(A) = (1/3) * 0.002 = 0.000667
* P(reply from B) = P(B) * R(B) = (1/2) * 0.001 = 0.0005
* P(reply from C) = P(C) * R(C) = (1/6) * 0.005 = 0.000833
* **Calculate the probability that the applicant has seen the job advertised in paper A, given only one reply:**
* P(A | one reply) = P(reply from A) / (P(reply from A) + P(reply from B) + P(reply from C))
* P(A | one reply) = 0.000667 / (0.000667 + 0.0005 + 0.000833)
* P(A | one reply) = 0.000667 / 0.002
* P(A | one reply) = 1/3
**Therefore, the probability that the applicant has seen the job advertised in paper A, given only one reply, is 1/3.**
**2. Probability that both applicants saw the job advertised in paper A, given two replies:**
* Assuming the replies are independent events:
* P(both replies from A) = P(reply from A) * P(reply from A)
* P(both replies from A) = 0.000667 * 0.000667
* P(both replies from A) = 0.000000444889
* **Calculate the probability that both applicants saw the job advertised in paper A, given two replies:**
* P(both A | two replies) = P(both replies from A) / (P(reply from any paper) * P(reply from any paper))
* P(both A | two replies) = 0.000000444889 / (0.002 * 0.002)
* P(both A | two replies) = 0.111222222
**Therefore, the probability that both applicants saw the job advertised in paper A, given two replies, is approximately 0.1112.**
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