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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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New post 09 Apr 2019, 17:48
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Difficulty:

  55% (hard)

Question Stats:

55% (02:20) correct 45% (02:08) wrong based on 22 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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New post 09 Apr 2019, 19:48
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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 = \(\frac{1}{12}*\frac{9}{10}*\frac{6}{7}=\frac{1*9*6}{12*10*7}=\frac{9}{140}\)

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

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New post 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
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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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