Testing for a disease can be made more efficient by combining samples. If the samples from fivefive people are combined and the mixture tests negative, then all fiveall five samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.10.1, find the probability of a positive result for fivefive samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?