We now take up the game Rat Race from The Price Is Right. Link: The Price Is Right - Rat Race
Game Description (Rat Race (The Price Is Right)): The game is played for three prizes: a small prize, a medium prize, and a car. There is a track with five wind-up rats (Pink, Orange, Blue, Red, Green). They will be set off on a race, where they will finish in (presumably) random order. The contestant has the opportunity to pick up to three of the rats: she guesses the price of three small items, and chooses one rat for each successful attempt. After the rats race, she wins prizes if one or more of her rats finish in the top three. If she picked the third place rat, she wins the small prize; if she picked the second place rat, she wins the medium prize; if he picked the first place rat, she wins the car. (Note that it is possible to win two or even all three prizes.)
Note that except for knowing the prices of the small items, there is no strategy. The rats are (we presume) equally likely to finish in any order. In this example, the contestant correctly prices two of the items and picks the pink and orange rats.
(a) Compute the probability that she wins the car.
(b) Compute the probability that she wins both the car and the meal delivery
(c) Compute the probability that she wins all three prizes