In a chemistry experiment, 1000 independent samples need to be tested for the presence of a chemical compound. To decrease the amount of testing, 5 samples at a time are combined and tested together. A combined sample will result in a negative test only if each of the five component samples is negative for the chemical compound.
If the probability of an individual sample testing positive is 0.2, what is the probability that a combined sample tests positive?
a. 0.6723
b. 0.3333
c. 0.5438
d. 0.8803
e. 0.2
