Question

A nationwide survey conducted by the National Cancer Society revealed the following information: Of 10,000 people surveyed, 3,300 were "heavy coffee drinkers' and 160 had cancer of the pancreas. Of those who had cancer of the pancreas, 137 were heavy coffee drinkers. Using the data in this survey, determine whether the events "being a heavy coffee drinker" and "having cancer of the pancreas" are independent events. not independent independent

Answer 1

`P(A \cap B) \\eq P(A)*P(B)`, so this events are dependent.

Explanation:

Two events, A and B, are independent if:

`P(A \cap B) = P(A)*P(B)`

In this problem, we have that:

Event A is being a heavy coffee drinker.

Of 10,000 people surveyed, 3,300 were "heavy coffee drinkers'. This means that
`P(A) = (3300)/(10000) = 0.33`

Event B is having cancer of the pancreas. Of 10,000 people surveyed, 160 had cancer of the pancreas. So
`P(B) = (160)/(10000) = 0.016`.

`A \cap B` is having cancer of the pancreas and being a heavy coffee drinker. Of 10000 people, 137 had cancer of the pancreas and were heavy coffee drinkers. So
`P(A \cap B) = (137)/(10000) = 0.0137`.

Now we verify if the equality is satisfied:

`P(A \cap B) = P(A)*P(B)`

`0.0137 = 0.016*0.033`

`0.0137 \\eq 0.000528`

`P(A \cap B) \\eq P(A)*P(B)`, so this events are dependent.