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?

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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?

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Answer 1 · 2015-05-16T22:23:59

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
$22$ $22$ Children
$49$ $49$ Adults

$71$ $71$ in total

we know that $12$ $12$ out of the $22$ $22$ children prefer chocolate.
so the probability of getting chocolate given that you are serving a child is $\frac{12}{22}$ $12/22$

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

Now we can observe that $\frac{12}{22} \neq \frac{43}{71}$ $12/22 != 43/71$

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 $P (x ∣ y) \neq P (x)$ $P(x|y)!=P(x)$ we know that the events are Dependent

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