A question on YA: "There are 120 customers in a store, 80 purchased at least 1 item. If 4 people are randomly selected, what's the probability all will buy at least 1 item?"
My Answer: The probability of any one customer having purchased an item is 80 out of 120 or 2/3. So if we are looking at parts of a whole, that represent all the possible combinations of events that could have occurred, then the part of this whole, where the first of the 4 people purchased an item, is 2/3 of the whole. Then the probability of finding a second person from the remaining crowd that also bought at least one item is 79 (because we already found one) out of 119 (again, because we have one less person to choose from in the crowd). The probability for the third person is found in a similar fashion...it would be 78/118 and 77/117 for the fourth person. We are each time finding an even smaller fraction of the whole that represents the final probability. If the probability for each was the same (independent events) then we could see that the area was decreasing exponentially (something I was never explicitly taught in school). To find the probability of all 4 people having bought at least 1 item, you need to find the product of the probabilities for each person. The answer then is 2/3 x 79/119 x 78/118 x 77/117 = approximately 19.25%.
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