In a triangle test one individual is asked to taste three similar appearing items and to choose the one with a different taste
than the other two. One of the three items has a different
composition from the other two. It may contain a preservative,
for example, but the other two items do not. Assume that three
individuals make their choices, which we assume to be independent, but the preservative cannot be detected by taste.
(a) What is the probability an individual correctly identifies
the item with the preservative by chance?
(b) What is the probability that at least two of the three
individuals identify the item with the preservative?
(c) If five individuals make a selection, what is the probability at least one will select correctly?