# Consider a two-way table that summarizes age and ice cream preference. Of the children, 7 prefer vanilla, 12 prefer chocolate, and 3 prefer butter pecan. Of the adults, 10 prefer vanilla, 31 prefer chocolate, and 8 prefer butter pecan. Are the events "chocolate" and "child" independent? Why or why not?

##### 1 Answer

One way to test if an event is independent is to check if the one event given the other, causes a different result.

If we are to calculate, we have in total

we know that

so the probability of getting chocolate given that you are serving a child is

now if we add up both the chocolate people for adults and children, we get

so

therefore, the probability of selling a chocolate ice cream is

Now we can observe that

which means that if you have a child coming to buy ice cream, it does have an effect on weather you will sell a chocolate ice cream.

thus we can say that the events are *Dependent*

as *Dependent*