Question

The Gift Basket Store had the following premade gift baskets containing the following combinations in stock.CookiesMugsCandyTotalCoffee57820Tea73313TOTAL12101133Choose 1 basket at random. Find the probability that it contains cookies given that it contains coffee (to three places after the decimal point).

Answer 1

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

`P(A|B)=(P(A\: and\: B))/(P(B))`

This means that the probability of event A given that event B has occurred.

For the given case, it becomes

`P(Cookies|Coffee)=(P(Cookies\: \: and\: \: Coffee))/(P(Coffee))`

The probability P(Cookies and Coffee) is the intersection of the column "Cookies" and the row "Coffee" divided by the grand total.

`P(Cookies\: \: and\: \: Coffee)=(5)/(33)`

The probability P(Coffee) is the row total of the row "Coffee" divided by the grand total.

`P(Coffee)=(20)/(33)`

Finally, the conditional probability is

`P(Cookies|Coffee)=(P(Cookies\: \: and\: \: Coffee))/(P(Coffee))=((5)/(33))/((20)/(33))=(5)/(33)\cdot(33)/(20)=(5)/(20)=(1)/(4)=0.25`

Therefore, the probability that it contains cookies given that it contains coffee is 0.25