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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. What is the probability that the next
couple the waiter seats will not order dessert?
However, 20% of the couples who order dessert don't order coffee. What is the probability that the next
couple the waiter seats will not order dessert?
- a)20%
- b)25%
- c)40%
- d)60%
- e)75%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The waiter at an expensive restaurant has noticed that 60% of the coup...
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:
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.
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.
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.
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.
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.
Most Upvoted Answer
The waiter at an expensive restaurant has noticed that 60% of the coup...
Given Information:
- 60% of couples order dessert and coffee.
- 20% of couples who order dessert do not order coffee.
Objective:
To find the probability that the next couple the waiter seats will not order dessert.
Approach:
Let's assume there are 100 couples in total. Based on the given information, we can break down the information as follows:
- 60 couples (60% of 100) order both dessert and coffee.
- 20 couples (20% of 100) order dessert but not coffee.
Now, we need to find the probability that the next couple the waiter seats will not order dessert. We can approach this by calculating the number of couples who do not order dessert and dividing it by the total number of couples.
Calculation:
- Number of couples who order both dessert and coffee = 60
- Number of couples who order dessert but not coffee = 20
To find the number of couples who do not order dessert, we subtract the number of couples who order both dessert and coffee and the number of couples who order dessert but not coffee from the total number of couples.
Number of couples who do not order dessert = Total number of couples - Number of couples who order both dessert and coffee - Number of couples who order dessert but not coffee
= 100 - 60 - 20
= 20
Therefore, out of 100 couples, 20 couples do not order dessert. Hence, the probability that the next couple the waiter seats will not order dessert is 20%.
Answer:
The probability that the next couple the waiter seats will not order dessert is 20% (option B).
- 60% of couples order dessert and coffee.
- 20% of couples who order dessert do not order coffee.
Objective:
To find the probability that the next couple the waiter seats will not order dessert.
Approach:
Let's assume there are 100 couples in total. Based on the given information, we can break down the information as follows:
- 60 couples (60% of 100) order both dessert and coffee.
- 20 couples (20% of 100) order dessert but not coffee.
Now, we need to find the probability that the next couple the waiter seats will not order dessert. We can approach this by calculating the number of couples who do not order dessert and dividing it by the total number of couples.
Calculation:
- Number of couples who order both dessert and coffee = 60
- Number of couples who order dessert but not coffee = 20
To find the number of couples who do not order dessert, we subtract the number of couples who order both dessert and coffee and the number of couples who order dessert but not coffee from the total number of couples.
Number of couples who do not order dessert = Total number of couples - Number of couples who order both dessert and coffee - Number of couples who order dessert but not coffee
= 100 - 60 - 20
= 20
Therefore, out of 100 couples, 20 couples do not order dessert. Hence, the probability that the next couple the waiter seats will not order dessert is 20%.
Answer:
The probability that the next couple the waiter seats will not order dessert is 20% (option B).
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