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probability + venn diagrams

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by prajanya » Wed Dec 15, 2010 1:53 pm
Q.) The waiter at an expensive resturant has noticed that 60% of the couples order desert and coffee. However, 20% of the couples who order desert dont order coffee. what is the probability that the next couple the waiter seats will not order desert?

A.) 20%
B.) 25%
C.) 40%
D.) 60%
E.) 75%

OA ...B
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by sachin2411 » Wed Dec 15, 2010 8:04 pm
This question can be solved only iff one will make an assumption that, couples have only two choice in the reastaurant, that is Desert and Coffee.

If this the case, then i have a solution. If not, then please some one provide the soution.
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by fitzgerald23 » Thu Dec 16, 2010 10:16 am
Set up a small chart as follows (assume 100 total people):


Dessert No Dessert Total
Coffee 60
No Coffee x
Total 60+x 100

In this case they tell us that the number who take dessert but no coffee is 20% of the total who order desert. So update your chart to be:

Dessert No Dessert Total
Coffee 60
No Coffee 0.2(60+x)
Total 60+x 100

Then solve

60 + 0.2(60+x)= 60 + x
60 + 12 +0.2x = 60 +x
12=0.8x
x= 15

So the total who ordered dessert is 75, making the number who choose not to order it 25.
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by sachin2411 » Thu Dec 16, 2010 11:04 am
yes, same assumption has been taken.
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by anshumishra » Thu Dec 16, 2010 11:16 am
As shown in the venn diagram , assuming there are 100 people.

x = (60+x)/5 (Since, 20% of the people who take desert don't take coffee)

=> x = 15

So, number of people who take only coffee = 40-x = 25

Hence the required probability = 25 %

Thanks
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by prachich1987 » Thu Dec 16, 2010 10:44 pm
sachin2411 wrote:This question can be solved only iff one will make an assumption that, couples have only two choice in the reastaurant, that is Desert and Coffee.

If this the case, then i have a solution. If not, then please some one provide the soution.
Eben if we don't assume that we can still answer the same way.
The question is " what is the probability that the next couple the waiter seats will not order desert?"
We can clearly find that 75% order desert.
So P(Those who don't order desert)=1-P(those who order desert)=1-0.75=0.25

Please advise if I am going wrong anywhere
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by sachin2411 » Thu Dec 16, 2010 11:04 pm
O yes, i was wrong, it can be solved without that assumption too.

Thanks for clarification.
prachich1987 wrote:
sachin2411 wrote:This question can be solved only iff one will make an assumption that, couples have only two choice in the reastaurant, that is Desert and Coffee.

If this the case, then i have a solution. If not, then please some one provide the soution.
Eben if we don't assume that we can still answer the same way.
The question is " what is the probability that the next couple the waiter seats will not order desert?"
We can clearly find that 75% order desert.
So P(Those who don't order desert)=1-P(those who order desert)=1-0.75=0.25

Please advise if I am going wrong anywhere
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by prachich1987 » Thu Dec 16, 2010 11:11 pm
sachin2411 wrote:O yes, i was wrong, it can be solved without that assumption too.

Thanks for clarification.
prachich1987 wrote:
sachin2411 wrote:This question can be solved only iff one will make an assumption that, couples have only two choice in the reastaurant, that is Desert and Coffee.

If this the case, then i have a solution. If not, then please some one provide the soution.
Eben if we don't assume that we can still answer the same way.
The question is " what is the probability that the next couple the waiter seats will not order desert?"
We can clearly find that 75% order desert.
So P(Those who don't order desert)=1-P(those who order desert)=1-0.75=0.25

Please advise if I am going wrong anywhere
I am posting a BTG link where a similar discussion is going on
Please refer to Q.2--But here the question is little different.we have to calculate % of people ordering coffee.
Plz share your thoughts
https://www.beatthegmat.com/fundamental- ... tml#324660
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by crisro » Tue Aug 21, 2012 7:36 am
If 20% of the couples who order dessert don't order coffee then 80% of the couples who order dessert order also coffee which is equal to 60% of all the couples.
80% dessert= 60% total
4 dessert = 3 total
dessert/total =3/4
no dessert/total = 1/4
Answer B
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