# Thread: prob word problem Q

1. ## prob word problem Q

A growing manufacturing company has kept careful records of applicants who have applied for jobs on their assembly lines. The probability that a new applicant will be called in for a first interview is 0.30, while the probability that he or she will be rejected outright is 0.45. Otherwise, the applicant is kept "on file". Of those applicants interviewed, some are rejected immediately, but the probability is 0.50 of being hired immediately and the probability is one in three of being called in for a second interview. Of the people interviewed a second time, half are hired and half are rejected. Of the people "on file", 80% are ultimately interviewed but the probability of one of those interviewees being hired is only 0.25.

a) what is the probability that an applicant for a job at this company's assembly line will be hired?

answer is 0.25

b) What is the probability that someone who is put "on file" is rejected?

answer is 0.80

c) what is the probability that someone who is interviewed is hired?

answer is 0.5
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so i tried drawing one of those famous tree/spider diagrams to help me solve this question but it doesnt seem to be working which is probably because there is a lot of information in this question and so my tree diagram isnt probably correct

but heres what i did to get my "incorrect" answers:

a) (0.3 first interview x 0.5 hired) + (0.333 second interview x 0.5 hired) + (0.8 interviewed from people on file x 0.25 hired) = 0.515

b) (0.55 on file x 0.8 interview x 0.25 hired) = 0.11

c) (0.3 first interview x 0.5 hired) + (0.333 second interview x 0.5 hired) = 0.3165

2. a) what is the probability that an applicant for a job at this company's assembly line will be hired?

(0.3 first interview x 0.5 hired) + (0.3 first interview x 0.333 second interview x 0.5 hired) + (0.25 on file x 0.8 interviewed from people on file x 0.25 hired) = 0.25

b) What is the probability that someone who is put "on file" is rejected?

(0.20 rejected) + (0.8 interview x 0.75 rejected) = 0.80

c) what is the probability that someone who is interviewed is hired?

taken right from the original question:
"Of those applicants interviewed, some are rejected immediately, but the probability is 0.50 of being hired immediately"

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