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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 02 Jun 2020, 07:33
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Question Stats:

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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 02 Jun 2020, 08:00
Given P of getting Job J = 2/5 ; K = 1/3 and S= 4/7
and not getting job J = 3/5 ; K = 2/3 and S = 3/7
and 25% or say 1/4 will get a Job
so the probability that only Kara receives a job offer out of the three friends
we have ; 1/4 * 3c1 * ( 1/3 * 3/5 * 3/7)
=> 3/140 *3c1 ; 9/140
OPTION B


Bunuel 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
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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 02 Jun 2020, 08:15
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Bunuel 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


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

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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 02 Jun 2020, 11:51
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IMO B

Probability of only Kara getting selected = (Probability of Kara getting selected for an interview * Probability of Kara getting selected for a job) *
(1- Probability of James getting selected for an interview * Probability of James getting selected for a job) *
(1- Probability of Smith getting selected for an interview * Probability of Smith getting selected for a job)


= (1/3 * 1/4) (1 - 2/5 * 1/4) (1 - 4/7* 1/4) = 1/3 * 1/4 * 9/10 * 6/7 = 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 02 Jun 2020, 11:54
Archit3110 wrote:
Given P of getting Job J = 2/5 ; K = 1/3 and S= 4/7
and not getting job J = 3/5 ; K = 2/3 and S = 3/7
and 25% or say 1/4 will get a Job
so the probability that only Kara receives a job offer out of the three friends
we have ; 1/4 * 3c1 * ( 1/3 * 3/5 * 3/7)
=> 3/140 *3c1 ; 9/140
OPTION B


Bunuel 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


why multiplied by 3c1 ? I did rest calc, getting 3/140, missed 3c1 multiplication, can u help
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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 06 Jun 2020, 04:27
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Bunuel 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


Solution:

The probability that only Kara receives a job offer out of the three friends is the probability that Kara receives a job offer AND James does not receive a job offer AND Smith does not receive a job offer. Because we use the word “and,” we will use the multiplication rule.

P(only Kara receives a job offer) = P(Kara receives a job offer) x P(James does not receive a job offer) x P(Smith does not receive a job offer)

Now let’s determine the probability of each.

P(Kara receives a job offer) = P(she gets an interview) x P(she gets the job offer, given that she’s gotten an interview) = 1/3 x 1/4 = 1/12

P(James does not receive a job offer) = P(he does not get an interview) + P(he gets an interview) x P(he doesn’t get the job offer given that he’s gotten an interview) = 3/5 + 2/5 x 3/4 = 3/5 + 3/10 = 9/10

P(Smith does not receive a job offer) = P(he does not get an interview) + P(he gets an interview) x P(he doesn’t get the job offer given that he’s gotten an interview) = 3/7 + 4/7 x 3/4 = 3/7 + 3/7 = 6/7

Therefore,

P(only Kara receives a job offer) = 1/12 x 9/10 x 6/7 = 1/2 x 9/10 x 1/7 = 9/140

Answer: B
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Re: James, Kara and Smith are three friends who have applied for a job at   [#permalink] 06 Jun 2020, 04:27

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

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