Опрос от журнала "8 часов": "Чем Вы питаетесь на работе?"
Комплексный обед в фирменной столовой
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GMAT/Problem Solving - Coffee and Dessert
Coffee and Dessert
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%
ОТВЕТЫ И КОММЕНТАРИИ
Решение
You can solve this problem with a matrix. Since the total number of diners is unknown and not important in solving the problem, work with a hypothetical total of 100 couples. Since you are dealing with percentages, 100 will make the math easier.
Set up the matrix as shown below:
Dessert
NO dessert
TOTAL
Coffee
NO coffee
TOTAL
100
Since you know that 60% of the couples order BOTH dessert and coffee, you can enter that number into the matrix in the upper left cell.
Dessert
NO dessert
TOTAL
Coffee
60
NO coffee
TOTAL
100
The next useful piece of information is that 20% of the couples who order dessert don't order coffee. But be careful! The problem does not say that 20% of the total diners order dessert and don't order coffee, so you CANNOT fill in 40 under "dessert, no coffee" (first column, middle row). Instead, you are told that 20% of the couples who order dessert don't order coffee.
Let x = total number of couples who order dessert. Therefore you can fill in .2x for the number of couples who order dessert but no coffee.
Dessert
NO dessert
TOTAL
Coffee
60
NO coffee
.2x
TOTAL
x
100
Set up an equation to represent the couples that order dessert and solve:
75% of all couples order dessert. Therefore, there is only a 25% chance that the next couple the maitre 'd seats will not order dessert. The correct answer is B.
Вверх 
