EXAMPLE 3.5.2

Recall this (authentic) data from the Natural Resources Defense Council:

40% of bottled water samples are merely tap water.

30% of bottled water samples are contaminated by such pollutants as arsenic and

fecal bacteria.

If two samples are independently selected, what is the probability

that both samples are contaminated by pollutants?

SOLUTION

Let E be the event that the first bottle is contaminated. Let F be the event that the second bottle is contaiminated. According to the statistics cited above, P(E) = .3, P(F) = .3, so