Chimpanzees have no known numbering system, but they may have a sense of quantity. To test this, a behavioral biologist presents a hungry chimp with 7 bunches of bananas containing, respectively, y=1, 2, 3, 4, 5, 6, 7 bananas. The chimp has been trained to understand that it may choose any 2 bunches of bananas.

a. How many combinations of 2 bunches are there?

b. Would this situation constitute sampling with or without replacement?

c. If it chooses at random, that is, it has no sense of quantity, what is the expected average number of bananas per bunch for the chimp's choice of two bunches? What is V()? What outcomes lie within two standard deviations of E()?

d. Suppose the chimp chooses the bunches with six and seven bananas. How many ways can this particular choice be made? What is the probability that this is just a random choice, meaning the chimp has no sense of quantity? Is there evidence that the animal has a sense of quantity?