Still More Probability
1. At Greg's Greaseburgers you can get your quarter pound burger on a white or whole wheat bun. All burgers come with ketchup, mustard, relish (and grease) as part of the standard burger. You can also get ONE of the following added to your burger for no extra charge: bacon, cheese, tomato, or onion. You do NOT have to have the extra item. Assume you can have multiple condiments, but you have to have at least one.
a. How many possible different burgers (as described above) can Greg make?
b. How many of the burgers have bacon or cheese?
c. Some college students always stop by Greg's after
a football game, so on football days he makes some burgers the minute the
game is over. He makes one of each burger in part a. If you
are first in line and randomly grab a burger, what is the probability that
you grab
i. a bacon burger?
ii. a burger with a wheat bun?
iii. a burger with a wheat bun that is also a bacon
burger?
iv. a bacon burger if you know that it has a wheat
bun?
v. a bacon burger if you know it has onions?
vi. a bacon burger or a cheeseburger
d. What are the odds against grabbing a bacon burger? What are the odds in favor of grabbing a bacon burger?
2. A mouse is in a maze. The maze has 9 decision
points. At each point the mouse can go either right or left. If the
mouse goes left at every decision point she gets to the cheese at the center
of the maze. If the mouse makes a random choice at each decision
point, find the probability that she
a. gets to the cheese?
b. doesn't get to the cheese?
c. makes exactly one wrong choice?
d. makes more than one wrong choice?
3. Another maze. This made has only 5 decision points,
but at each one the mouse can go right, left, or straight. this time going
to the right every time gets the mouse to the cheese. If the mouse
makes a random choice at each decision point, find the probability that
he
a. gets to the cheese
b. doesn't get to the cheese
c. makes at least three wrong choices?