The waiter at an expensive restaurant has noticed that 60%

Probably the best way to solve this question is using the double set matrix, as shown below:



From above, we have that 60+0.2x=x --> x=75.

Thus, the probability that the next couple will not order dessert (yellow box) is 100-75=25.

Answer: B.

Hope it's clear.


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Let total number of couples be 100.

60% order Dessert & Coffee = 60 couples.
20% who order Dessert do not order coffee => 80% who order dessert also order coffee this is given to be 60.
Hence total number of couples who order Dessert is 60*100/80 = 75.
Number of couples who do NOT order Dessert = 100-75 = 25.
The probability that next order will not have dessert is 25%.

Let the number of people ordering only desert = d, only ordering coffee be c and ordering both be b. Given that , 20 % of (b+d) = d

or 4d = b.

Thus, as b = 60, d = 15. The total number of people not ordering desert = 100-(60+15) = 25.

B.
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I solved this pretty fast this way:

60% dessert and coffee
--> 40% nothing, dessert, or coffee

Let them be the same probability --> 40% / 3 = 13,333%

40% - 13% = 27% --> Answer has to be around this range --> B is closest

60% order (C+D) i.e Both = 60% of Total
20% of D is without C; i.e. 80% of D also orders C
80% of D = Both
80% of D = 60% of Total
\(\frac{D}{Total} =\frac{60}{80} = \frac{3}{4}\)
Hence, \(\frac{C}{Total} = \frac{1}{4}\) = 25%

You can use the following equation:

Total = Dessert only + Coffee only + Both + Neither

Instead of using percents, let’s use numbers. If we let the total number of customers be 100, then we see that 60 of them will order dessert and coffee:

100 = D + C + 60 + N

Since we have let D = the number of couples ordering Dessert only, we know that the total number of couples ordering Dessert is (D + 60), which is “Dessert only” plus “Both.”. Since 20% of the couples who order dessert don't order coffee, that means “Dessert only” is 20% of the total of “Dessert only” and “Both;” that is,

D = 0.2(D + 60)

5D = D + 60

4D = 60

D = 15

Substituting, we have:

100 = 15 + C + 60 + N

100 = 75 + C + N

25 = C + N

Since those who don’t order dessert are the total of “Coffee only” and “Neither,” we have 25% of the couples who don’t order dessert.

Answer: B
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Solving for X in the figure shown below we will get Couples for deserts as 75%
And couples not ordering deserts =100-75=25%

Let, total dessert ordered = T and total couple = 100
From question,
60+20% of T = T
or, T = 75 % ordered dessert.

So next couple will not order dessert = 100-75 = 25 %

let total couples=100
let d=couples who order dessert
d-60=.2d
d=75 couples
100-75=25 couples who don't order dessert
25/100=25%

what about (Neither) those who didnt order coffee nor desert

To get the probability that the next couple will not order dessert we need the percentage of those who do not order dessert which is 25. Those 25% include Coffee/No Dessert and No Coffee/No Dessert (Neither).
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Please help me to understand why is the equation is 60+0.2x = x.
Why shouldn't it be solved as
60 + 20 = x.

Posted from my mobile device

We are given that 20% of the couples who order dessert don't order coffee. We denoted those who order dessert by x, thus those who order dessert but don't order coffee is 20% of that, which is 0.2x.
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there are 3 cases here:
1) dessert = D (this includes couples who order only dessert + couples who order dessert and coffee)
2) dessert and coffee = b
3) coffee = C (this includes couples who order only coffee + couples who order dessert and coffee)

We have been told that 60% of couples order both.
=> b is a an intersection of D & C

Also, mentioned in the question is that 20% couples order dessert only but not coffee. If you rephrase it, it means 80% of couples who order dessert also order coffee.

Now let's consider total # couples as 100 (as percentage numbers can be used as is without any conversion)

=> b = 60 => 80% of D=60 => D=75
That tells us that 75 couples out of 100 i.e 75% couples order desserts, that means 25% dont order dessert which is the probability asked.

Answer is 25% (B)

Here please note that no where it is mentioned in the question stem that every couple orders at least a dessert or a coffee or both. So we need to consider the possibility that few couples order nothing. So don't split the numbers as only dessert =20,both= 60, only coffee =20. This is wrong

Here 25% includes only coffee + neither

Posted from my mobile device

Given: The waiter at an expensive restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee.

Asked: What is the probability that the next couple the waiter seats will not order dessert?

	Dessert	˜Dessert	Total
Coffee	.8x%=60%
˜Coffee	.2x%
Total	x%

.8x% = 60%
x = 60/.8 = 75

	Dessert	˜Dessert	Total
Coffee	.8x%=60%
˜Coffee	.2x% = 15%
Total	x%=75%	100%-75%=25%	100%

The probability that the next couple the waiter seats will not order dessert = 25%

IMO B