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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Of the 20 members of a kitchen crew, 17 can use the
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22 Sep 2016, 12:30
22 Sep 2016, 12:30
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Question Stats:
85% (00:54) correct
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Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?
a) 0
b) 1/10
c) 1/7
d) 1/4
e) 1/3
a) 0
b) 1/10
c) 1/7
d) 1/4
e) 1/3
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Of the 20 members of a kitchen crew, 17 can use the
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22 Sep 2016, 12:31
22 Sep 2016, 12:31
1
GreenlightTestPrep wrote:
Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?
a) 0
b) 1/10
c) 1/7
d) 1/4
e) 1/3
a) 0
b) 1/10
c) 1/7
d) 1/4
e) 1/3
Here's a step-by-step approach using the Double Matrix method.
Here, we have a population of kitchen staff, and the two characteristics are:
- can use the meat-cutting machine or cannot use the meat-cutting machine
- can use the bread-slicing machine or cannot use the bread-slicing machine
There are 20 people altogether, so we can set up our diagram as follows:
Given: 17 can use the meat-cutting machine
This means that 3 cannot use the meat-cutting machine
We'll add this to our diagram:
Given: 18 can use the bread-slicing machine
This means that 2 cannot use the bread-slicing machine
We'll add this to our diagram:
Given: 15 can use both machines
We'll add this to our diagram:
Since we know the SUMS of the boxes in each column and in each row, we can complete the diagram as follows:
As we can see, there are 0 people in the box representing someone who cannot use either machine.
So, P( selected person cannot use either machine) = 0/20 = 0
Answer:
Show: ::
A
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Re: Of the 20 members of a kitchen crew, 17 can use the
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29 Sep 2018, 09:12
29 Sep 2018, 09:12
1
Can I use Venn diagram to solve this.. In first circle 17. Second one 18 n in between 15.. so we can conclude that people who use only meat machine are two and people who use only the bread machines are 3 and 15 use both so there is no member who does not use these machine. Hence 0/20.. Let me know if its correct.
