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1. Suppose A, B, and C are events such that P(A) = 0:5, P(B) = 0:2, and P(C) = 0:1. (a) If A, B, and C are all mutually exclusive, what is the
1. Suppose A, B, and C are events such that P(A) = 0:5, P(B) = 0:2, and P(C) = 0:1.
(a) If A, B, and C are all mutually exclusive, what is the probability that at least
one of A, B, or C occurs?
(b) If A, B, and C are all independent, what is the probability that at least one of
A, B, or C occurs?
2. Two dice are rolled, and we add the numbers appearing on top.
(a) Show that the event that the sum is 10 is independent of the event that the rst
die is 5.
(b) Show that the event that the sum is 10 is not independent of the event that at
least one die is 5.
3. Hontie Maul hosts a game show where a contestant views three doors, two of which
have a beautiful new car (and one of which has an unattractive goat). Assume you are
a contestant on this show who prefers cars over goats.
You choose one door, and Hontie Maul opens a second door and says, Check this out!
Here is a car that you can't have: you could have picked this door, but you didn't.
Would you like to switch to the other door?" How do you reply?
4. It is estimated that 4% of the U.S. population are sociopaths. Of sociopaths who take
a Facebook Are you a sociopath?" test, 100% pass the test. On the other hand, of
non-sociopaths who take it, 20% pass the test.
You are about to go on a blind date with someone, about whom you know nothing
else, who takes the test and passes. What is the probability that s/he actually is a
sociopath?
