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kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
05 Mar 2019, 01:35
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:27) correct
42%
(02:54)
wrong
based on 316
sessions
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According to study in an office, 12 out of 30 employees were interested in doing work from home, if 3 employees were selected random, what is the probability that at most 2 of them were interested in doing work from home?
A. 11/203
B. 192/203
D. 64/65
D. 1/203
E. None of these
A. 11/203
B. 192/203
D. 64/65
D. 1/203
E. None of these
05 Mar 2019, 23:21
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kiran120680
We are selecting 3 employees and want at most 2 of them to be interested in doing work from home. At most 2 means 0, 1 or 2. So, any number but 3. Let's calculate the opposite probability and subtract that from 1.
APPROACH 1:
\(P(at \ most \ 2) = 1 - P(3) = 1 - \frac{12}{30}*\frac{11}{29}*\frac{10}{28} = \frac{192}{203}\).
Answer: B.
APPROACH 2:
\(P(at \ most \ 2) = 1 - P(3) = 1 - \frac{12C3}{30C3} = \frac{192}{203}\).
Answer: B.
General Discussion
06 Mar 2019, 11:13
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The method I did in is much longer but might be helpful
Atmost 2 means selecting 0, 1 , 2.
So case 1: we select 2 employees interested in work from home(wfh) and 1 employee mot interested in wfh
12c2*18c1
Case 2: we select 1 employee interested in work from home(wfh) and 2 employees mot interested in wfh
12c1*18c2
Case 3: we select 0 employees interested in work from home(wfh) and 3 employees mot interested in wfh
12c0*18c3
Therefore probability of atmost 2 people who want wfh being selected in 3 is sum of case 1,2 and 3, divided by total possibility of choosing any 3 people.
(12c2*18c1+12c1*18c2+12c0*18c3)/30c3
= 192/203
IMO B
Posted from my mobile device
Atmost 2 means selecting 0, 1 , 2.
So case 1: we select 2 employees interested in work from home(wfh) and 1 employee mot interested in wfh
12c2*18c1
Case 2: we select 1 employee interested in work from home(wfh) and 2 employees mot interested in wfh
12c1*18c2
Case 3: we select 0 employees interested in work from home(wfh) and 3 employees mot interested in wfh
12c0*18c3
Therefore probability of atmost 2 people who want wfh being selected in 3 is sum of case 1,2 and 3, divided by total possibility of choosing any 3 people.
(12c2*18c1+12c1*18c2+12c0*18c3)/30c3
= 192/203
IMO B
Posted from my mobile device
