Question

A chemist analyzes seawater samples for two heavy metals: lead and mercury. Past experience indicates that 38% of the samples taken from near the mouth of a river on which numerous industrial plants are located contain toxic levels of lead or mercury; 32% contain toxic levels of lead and 16% contain toxic levels of mercury

What is the probability that a randomly selected sample will not contain lead or will not contain mercury?

Answer 1

Solution:

Given: 38% of the samples taken from near the mouth of a river on which numerous industrial plants are located contain toxic levels of lead or mercury.

That is: P( contain toxic levels of lead or mercury ) = 38% = 0.38

32% contain toxic levels of lead

That is: P( contain toxic levels of lead) = 32% = 0.32

and

16% contain toxic levels of mercury

P( contain toxic levels of mercury) = 16% = 0.16

Let A = contain toxic levels of lead and B = contain toxic levels of mercury

Thus we have:

P( A or B ) = P( A U B ) = 38%

P(A) =0.32

P(B) = 0.16

We have to find:

P( a randomly selected sample will not contain lead or will not contain mercury) = ............?

That is we have to find:

De'Morgans law is:

Thus

Thus first we need to find:

Using addition rule of probability, we get:

Thus