1. (10 points)

A fair two sided coins is flipped three times. Find the probability for each of the following possible occurances:

a) the 2nd flip lands heads, while the 1st and 3rd land tails

b) the last flip is heads

c) the first flip lands differently from the last flip

d) two flips in row or more come up the same way

2. (10 points)

Consider the roll of two 6-sided fair dice. The sum of the two top faces of the dice can be any integer between 2 and 12. Calculate the probability that upon rolling the dice, they land with their sum equal to N = 2, 3, 4, ..., 12. Make a graph of this probability versus N.

3. (10 points)

Among ten students eligible to serve on a certain committee, two are sophomores, four juniors, and four seniors. If a committee of four is chosen at random, what is the probability that it will consist of

a) two juniors and two seniors?

b) one sophomore, two juniors, and one senior?

c) all seniors?