Conditional probability:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
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.
[tex]P(A\cap B)=P(Hot\cap Large)=22[/tex]
• The probability of a large (event B) is the addition of all the possibilities of ordering large:
[tex]P(B)=P(Large)=22+5=27[/tex]
Finally, we replace these values in the formula:
[tex]P(Hot|Large)=\frac{P(Hot\cap Large)}{P(Large)}[/tex][tex]P(Hot|Large)=\frac{22}{27}[/tex]
Answer:
[tex]P(Hot|Large)\approx0.81[/tex]
