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
May 16, 2015

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