Respuesta :
We are asked to find the probability that it contains cookies given that it contains coffee.
This is called conditional probability and is given by
[tex]P(A|B)=\frac{P(A\: and\: B)}{P(B)}[/tex]This means that the probability of event A given that event B has occurred.
For the given case, it becomes
[tex]P(Cookies|Coffee)=\frac{P(Cookies\: \: and\: \: Coffee)}{P(Coffee)}[/tex]The probability P(Cookies and Coffee) is the intersection of the column "Cookies" and the row "Coffee" divided by the grand total.
[tex]P(Cookies\: \: and\: \: Coffee)=\frac{5}{33}[/tex]The probability P(Coffee) is the row total of the row "Coffee" divided by the grand total.
[tex]P(Coffee)=\frac{20}{33}[/tex]Finally, the conditional probability is
[tex]P(Cookies|Coffee)=\frac{P(Cookies\: \: and\: \: Coffee)}{P(Coffee)}=\frac{\frac{5}{33}}{\frac{20}{33}}=\frac{5}{33}\cdot\frac{33}{20}=\frac{5}{20}=\frac{1}{4}=0.25[/tex]Therefore, the probability that it contains cookies given that it contains coffee is 0.25
