Question

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?

Answer 1

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
`22` Children
`49` Adults

`71` in total

we know that `12` out of the `22` children prefer chocolate.
so the probability of getting chocolate given that you are serving a child is `12/22`

now if we add up both the chocolate people for adults and children, we get `12 + 31= 43`
so `43` out of the total amount of customers prefer chocolate.
therefore, the probability of selling a chocolate ice cream is `43/71`

Now we can observe that `12/22 != 43/71`

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 `P(x|y)!=P(x)` we know that the events are Dependent