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James, Kara and Smith are three friends who have applied for a job at
[#permalink]
20 Oct 2021, 09:17
20 Oct 2021, 09:17
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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
A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175
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Re: James, Kara and Smith are three friends who have applied for a job at
[#permalink]
20 Oct 2021, 09:44
20 Oct 2021, 09:44
1
Carcass wrote:
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
A. 1/12
B. 9/140
C. 1/42
D. 27/2240
E. 2/175
P(only Kara gets offer) = P(Kara gets job offer AND James gets NO job offer AND Smith gets NO job offer)
= P(Kara gets job offer) x P(James gets NO job offer) x P(Smith gets NO job offer)
Let's calculate each probability separately:
P(Kara gets job offer)
P(Kara gets job offer) = P(gets interview AND receives job offer)
= P(gets interview) x P(receives job offer)
= 1/3 x 1/4 (since the company offers a job to only 25% of interviewees)
= 1/12
P(James gets NO job offer)
P(James gets NO job offer) = P(gets interview AND receives NO job offer OR doesn't get interview)
= P(gets interview) x P(receives NO job offer) + P(doesn't get interview)
= (2/5 x 3/4) + 3/5
= 3/10 + 3/5
= 9/10
P(Smith gets NO job offer)
P(Smith gets NO job offer) = P(gets interview AND receives NO job offer OR doesn't get interview)
= P(gets interview) x P(receives NO job offer) + P(doesn't get interview)
= (4/7 x 3/4) + 3/7
= 3/7 + 3/7
= 6/7
So.....
P(only Kara gets offer) = P(Kara gets job offer) x P(James gets NO job offer) x P(Smith gets NO job offer)
= 1/12 x 9/10 x 6/7
= 54/840
= 9/140
Answer: B
Cheers,
Brent
gmatclubot
Re: James, Kara and Smith are three friends who have applied for a job at [#permalink]
20 Oct 2021, 09:44
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