Question

The table below shows the number of different drinks ordered at a coffee morning.

One of the drinks is chosen at random.
a) Work out P(small coffee).
b) Work out P(coffee small).
Give each answer as a fraction in its simplest form.

Answer 1

Given that one of the drinks is chosen at random:

a) P(small | coffee) = 6/13

b) P(coffee | small) = 3/11

How to calculate the probabilities

To calculate the probabilities, use the following notation:

P(small) represents the probability of choosing a small drink.

P(coffee) represents the probability of choosing coffee.

a) To find P(small | coffee), which is the probability of choosing a small drink given that the drink chosen is coffee, use the formula:

P(small | coffee) = P(small and coffee) / P(coffee)

From the table, the number of small coffees is 6, and the total number of drinks is 34. Therefore:

P(coffee) = 13/34

The number of small coffees is 6, and the total number of small drinks is 22. Therefore:

P(small and coffee) = 6/34

Now substitute these values into the formula:

P(small | coffee) = (6/34) / (13/34) = 6/13

b) To find P(coffee | small), which is the probability of choosing coffee given that the drink chosen is small, use the formula:

P(coffee | small) = P(coffee and small) / P(small)

From the table, the number of small coffees is 6, and the total number of small drinks is 22. Therefore:

P(small) = 22/34

The number of small coffees is 6, and the total number of drinks is 13. Therefore:

P(coffee and small) = 6/34

Now we can substitute these values into the formula:

P(coffee | small) = (6/34) / (22/34) = 6/22 = 3/11

Therefore, the answers are:

a) P(small | coffee) = 6/13

b) P(coffee | small) = 3/11