Probability

ronaldramlan wrote:The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability that the next couple the maitre 'd seats will not order dessert?

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

Go ahead ...

Let total people = 100.

We can plug in the answers, which represent the number out of the total 100 people who do not order dessert.

Answer choice C: 40 do not order dessert.
Thus, the total number who order dessert = 60.
Too small.
Since not everyone who orders dessert also orders coffee, the total number who order dessert must be greater than the number who order both dessert and coffee (60).
To increase the the total number who order dessert, the number who do not order dessert must be smaller.
Eliminate C, D and E.

Answer choice B: 25 do not order dessert.
Thus, the total number who order dessert = 75.
Number who order dessert but not coffee = (.2)*75 = 15.
Thus, number who order both dessert and coffee = 75-15 = 60.
Success!

The correct answer is B.

D and C = 60
D, but not C=20

so no. of people who will order desert is atleast 80
No. of people who will not order desert = (100-80)/100 = 20/100 = 1/5 = 20 %

IMO:A

OA and OE please!

Here i go

if 20% of couples who order desserts don't order coffee then 80% order both. hence 60% is actually 80% of those who order both.

if we consider total 100 then.
0.8x=60 (where x is the number of people who order desserts)

hence x=75
so the number of people who don't order desserts will be 25 (100-75)

hence probability that next couple will not order dessert will be
25/100
25% (B)