Question

Gwen has recently purchased a cottage. She has arranged
to have well dug on the property. One in five wells that
were dug recently in the vicinity were dry, and 30% of the
others were contaminated. Find the probability of each of
the following:

a) Gwen’s well will not be dry.

(b) Gwen’s well will be uncontaminated, given that it is not dry.

(c) Gwen will have safe drinking water
from her well.
(d) Gwen will not have safe-drinking
water from her well.

Answer 1

A) 0.8
B) 0.24
C) 0.56
D) 0.44

For A, since 1 in 5 is dry, 4 in 5 are not; 4/5 = 0.8

For B, we know that 30%, 0.3, of the ones that are not dry are contaminated:
0.3(0.8) = 0.24

For C, 100%-30%=70% of wells that are not dry are not contaminated; 0.7(0.8) = 0.56

For D, she will either have contaminated water or no water:
0.24+0.2 = 0.44