Problem #1.
A box contains 6 red marbles, 2 blue marbles, and 2 green marbles.  Three are drawn without replacement.  Let X count the number red marbles drawn.  Is X distributed as a binomial?

Problem #2.
A box contains 6 red marbles, 2 blue marbles, and 2 green marbles.  The roll of a die determines the number that are drawn with replacement.  Let X count the number red marbles drawn.  Is X distributed as a binomial?

Problem #3.
A box contains 6 red marbles, 2 blue marbles, and 2 green marbles.  Three are drawn with replacement.  Let X count the number red marbles drawn.  Is X distributed as a binomial?


Problem #4.
According to a Univ. of New Hampshire poll, 10% of US adults believe the earth is flat.  (I always wonder what their theory of gravity is.  Put a bunch of stuff together with similar velocities and they clump into a sphere.)

Assume you pick a simple random sample of 10 American adults.

a.  What's the prob they all believe the earth isn't flat?
b.  How about exactly 2 believe the earth is flat.
c.  Prob that 2 or less believe the earth is flat.
d.  What's the expected number of flat-earthers?

Problem #5.
In a certain game, the probability of winning is 35%.  In five games, find the probability . . .

a.  . . . of losing them all 5.
b.  . . . .of losing all but 1 or 2.
c.    What's the expected number of wins?