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01 Jun 2022, 05:45
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Difficulty:
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59% (02:52) correct
41%
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wrong
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James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5, 1/3 and 4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?
A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175
Are You Up For the Challenge: 700 Level Questions
A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175
Are You Up For the Challenge: 700 Level Questions
Shhh103
Joined: 14 Oct 2021
Last visit: 23 Mar 2023
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Affiliations: edtech lIMITED
Location: India
Concentration: Finance, General Management
Schools: IIMA PGPX"20 Harvard '24 (D) Stanford '24 Haas '24
GMAT 1: 530 Q47 V17
GMAT 2: 670 Q49 V32
GPA: 3.06
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02 Jun 2022, 09:59
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probability of Kara clear 1st & 2nd round = 1 st round she clear * second round
1/3 * 1/4 (25% given)= 1/12
probability of james not clear in first round= 1-2/5 = 3/5
or probability of james selected in first round & rejected in second round = 2/5 * 3/4 (75%) given = 3/10
so james not clearing = 3/5 + 3/10 = 9/10
probability of smith not clear first round = 3/7
probability of smith clear first but fail in second = 4/7 * 3/4 (75%) = 3/7
probability of smith failing = 3/7 + 3/7 = 6/7
probablity of only kara = 1/12 * 9/10 * 6/7 = 9/140
give kudos if you find it useful
1/3 * 1/4 (25% given)= 1/12
probability of james not clear in first round= 1-2/5 = 3/5
or probability of james selected in first round & rejected in second round = 2/5 * 3/4 (75%) given = 3/10
so james not clearing = 3/5 + 3/10 = 9/10
probability of smith not clear first round = 3/7
probability of smith clear first but fail in second = 4/7 * 3/4 (75%) = 3/7
probability of smith failing = 3/7 + 3/7 = 6/7
probablity of only kara = 1/12 * 9/10 * 6/7 = 9/140
give kudos if you find it useful
03 Jun 2022, 03:42
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This post is very much in line with the above approach.
However, there's a scope to reduce calculation IMHO.
The required probability = Probability of Kara getting the job × Probability of James NOT getting the job × Probability of Smith NOT getting the job
The answer is B.
However, there's a scope to reduce calculation IMHO.
- The required probability asks for the scenario when Kara receives the job and the other two do not.
The probability of Kara receiving the job = \(\frac{1}{3}×\)\(\frac{1}{4}\) =\(\frac{1}{12}\)
The probability of James receiving the job = \(\frac{2}{5}×\)\(\frac{1}{4}\) =\(\frac{1}{10}\)
The probability of Smith receiving the job = \(\frac{4}{7}×\)\(\frac{1}{4}\) =\(\frac{1}{7}\)
The required probability = Probability of Kara getting the job × Probability of James NOT getting the job × Probability of Smith NOT getting the job
- =\(\frac{1}{12}\) × (1 - \(\frac{1}{10}\)) × (1 - \(\frac{1}{7}\))
= \(\frac{1}{12}\) × \(\frac{9}{10}\) × \(\frac{6}{7}\)
=\(\frac{9}{140}\)
The answer is B.
