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
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)
=
1/12P(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
=
9/10P(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
=
6/7So.....
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