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# James, Kara and Smith are three friends who have applied for a job at

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James, Kara and Smith are three friends who have applied for a job at  [#permalink]

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09 Apr 2019, 17:48
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3
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Difficulty:

55% (hard)

Question Stats:

59% (02:28) correct 41% (02:07) wrong based on 27 sessions

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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

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Re: James, Kara and Smith are three friends who have applied for a job at  [#permalink]

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09 Apr 2019, 19:48
2
aragonn 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

So there is a 25% or 1/4 chance of being making it and 3/4 chance of not making it if called for interview....
Kara making it... ( Called for interview)*(making it in the interview)=$$\frac{1}{3}*\frac{1}{4}=\frac{1}{12}$$..
James making it... ( Called for interview)*(making it in the interview)=$$\frac{2}{5}*\frac{1}{4}=\frac{1}{10}$$, so $$\frac{9}{10}$$ of not making it.
Smith making it... ( Called for interview)*(making it in the interview)=$$\frac{4}{7}*\frac{1}{4}=\frac{1}{7}$$, so $$\frac{6}{7}$$ of not making it.

So, Probability of only Kara making it = $$\frac{1}{12}*\frac{9}{10}*\frac{6}{7}=\frac{1*9*6}{12*10*7}=\frac{9}{140}$$

B
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Re: James, Kara and Smith are three friends who have applied for a job at  [#permalink]

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11 Apr 2019, 10:10
aragonn 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

good question

P of 25 % ; 1/4 chance
so for getting a job
J = 2/5 * 1/4 ; 1/10 ; no job ; 9/10
K = 1/3 * 1/4 ; 1/12 ; no job ; 11/12
S= 1/4 * 4/7 ; 1/7 ; no job ; 6/7
so P (K) gets job ; 1/12 * 6/7*9/10
solve we get 9/140
IMO B
Re: James, Kara and Smith are three friends who have applied for a job at   [#permalink] 11 Apr 2019, 10:10
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