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From a group of 8 volunteers, including Andrew and Karen, 4
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27 Aug 2020, 09:56
27 Aug 2020, 09:56
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From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?
A. 3/7
B. 5/12
C. 27/70
D. 2/7
E. 9/35
A. 3/7
B. 5/12
C. 27/70
D. 2/7
E. 9/35
Re: From a group of 8 volunteers, including Andrew and Karen, 4
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27 Aug 2020, 09:56
27 Aug 2020, 09:56
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Re: From a group of 8 volunteers, including Andrew and Karen, 4
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27 Aug 2020, 10:25
27 Aug 2020, 10:25
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Carcass wrote:
From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?
A. 3/7
B. 5/12
C. 27/70
D. 2/7
E. 9/35
A. 3/7
B. 5/12
C. 27/70
D. 2/7
E. 9/35
P(Andrew is selected but Karen is not selected) = (number of 4-person groups with Andrew but not Karen)/(total # of 4-person groups possible)
number of 4-person groups with Andrew but not Karen
Take the task of creating groups and break it into stages.
Stage 1: Place Andrew in the 4-person group
We can complete this stage in 1 way
Stage 2: Send Karen out of the room and, from the remaining 6 volunteers, select 3 more people.
Since the order in which we select the 3 volunteers does not matter, we can use combinations.
We can select 3 people from 6 volunteers in 6C3 ways (20 ways).
the video below shows you how to calculate combinations (like 6C3) in your head
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 4-person group) in (1)(20) ways (= 20 ways)
total # of 4-person groups possible
We can select 4 people from all 8 volunteers in 8C4 ways ( = 70 ways).
So, P(Andrew is selected but Karen is not selected) = (20)/(70)
= 2/7
Answer: D
Cheers,
Brent
