Question

To reduce laboratory​ costs, water samples from five public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past​ results, there is a 0.007 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from five public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

Answer 1

Answer:

Step-by-step explanation:

Given that:

The numbers of the possible public swimming pools are 5

From past results, we have 0.007 probability of finding bacteria in a public swimming area.

In the public swimming pool, the probability of not finding bacteria = 1 - 0.007

= 0.993

Thus;

Probability of combined   =  Probability that at least one public

sample with bacteria           swimming area have bacteria

Probability of combined sample with bacteria  = 1 - P(none out of 5 has          

                                                                                bacteria)

   

Probability of combined sample with bacteria = 1 - (0.993)⁵        

= 1 - 0.9655

= 0.0345

Thus, the probability that the combined sample from five public swimming areas will show the presence of bacteria is 0.0345

From above, the probability that the combined sample shows the presence of bacteria is 0.0345 which is lesser than 0.05.

Thus, we can conclude that;  Yes, the probability is low enough that there is a need for further testing.