Suppose my grocery store of choice has 20 shopping carts in total and 10 of themhave wobbly wheels (they don’t really push properly). I’ve gone to the store with3 of my friends to stock up for a big party and we decide to split up (each of ustaking a cart, so 4 carts in total). Let X be the number of carts with wobbly wheels (out of the 4 me and my friends have taken).
a. What is the distribution of X?
b. Give the name of the distribution and the appropriate parameters.
c. What is the mean and variance of this distribution?
d. Give your answer as a number, but include the formulas (or logic) used.
e. What is the probability exactly 2 of us have carts with wobbly wheels?
f. What is the probability that at least 1 of us has a cart with wobbly wheels?