Question

What is the conditional probability that a customer ordered a hot drink given that he or she ordered a large?

Answer 1

Conditional probability:

`P(A|B)=(P(A\cap B))/(P(B))`

The probability that A occurs given that B has occurred is given in the formula above.

As in our problem we are asked for the probability that a customer ordered a hot drink (event A) given that he or she ordered a large (event B), then we can work with the formula.

• The union between hot drink and large can be written as follows, and this is equal to 22 as we can see in the table.

`P(A\cap B)=P(Hot\cap Large)=22`

• The probability of a large (event B) is the addition of all the possibilities of ordering large:

`P(B)=P(Large)=22+5=27`

Finally, we replace these values in the formula:

`P(Hot|Large)=(P(Hot\cap Large))/(P(Large))`
`P(Hot|Large)=(22)/(27)`

Answer:

`P(Hot|Large)\approx0.81`