Question

The probability of finding

E coli at a randomly selected beach is 0.005. To save money, the

DNR people combine five samples before

running a test: if it comes up negative, they've killed five

birds with one stone

though if it comes out positive, they have to go back and test each of the

five beaches individually. Find the probability of a positive test result when combining five

samples at random.

Answer 1

Given that probability of finding e-coli in a randomly selected beach is p=0.005
Probability of not finding e-coli in a randomly selected beach is 1-p= 1-0.005 = 0.995

Positive test result will come if atleast 1 of the 5 beaches have e-coli.

Probability of positive test result = Probability of having e-coli in atleast 1 of the 5 beaches.

=>1- probability of having e-coli in none of the 5 beaches = 1- (0.995)^5 = 0.0247.

Therefore, the required probability of getting a positive result when combining 5 samples at random is 0.0247.