Question

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?

Answer 1

Answer: P' = 0.25 or 25%

Therefore, the probability that the next couple would not order dessert is 25%

Explanation:

Given;

Percentage of those that order dessert and coffee = 60%

Percentage of those that order dessert = x ( let x represent percentage of those that orders dessert)

Percentage of those that order dessert and not coffee = 20% of x = 0.2x

The total percentage x of those tgat order dessert is

x = 60% + 20 % of x

x = 0.6 + 0.2x

x - 0.2x= 0.6

x = 0.6/0.8

x = 0.75

The total fraction of those that orde dessert is x = 0.75

The probability that the next couple would not order dessert P' is given as

P' = f'

Where f' is the fraction of those that don't order dessert.

f' = 1 - x = 1 - 0.75 = 0.25

P' = 0.25 or 25%

Therefore, the probability that the next couple would not order dessert is 25%

Answer 2

25%

Explanation:

60% of couples ordered dessert and coffee

20% of the couples ordered dessert but not coffee.

Let x be the total number of couples that ordered dessert.

Let y be the total number of couples that did not order dessert.

Couple that ordered dessert but not coffee = 20% * x

= 0.2x

60 + 0.2x = x

60 = x - 0.2x

60 = 0.8x

x = 60/0.8

x = 75

Total no of couples that ordered dessert and didn't order dessert = 100

x + y = 100

75 + y = 100

y = 100 - 75

y = 25%

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