Analysis of Algorithms : An Active Learning Approach

1.3 MATHEMATICAL BACKGROUND 19

the column represents another. (Because we assume that you will toss two

different dice, the diagonal of this matrix should be left blank because it

represents matching a die against itself.) These dice have an interesting

property—can you determine it?

5. There are five coins on the table. You choose one at random and flip it. For
   each of the four cases below, what is the chance that the majority of coins
   will be tails when you are done?
   a. Two heads and three tails c. Four heads and one tail
   b. Three heads and two tails d. One head and four tails


6. There are five coins on the table. Each coin is flipped exactly once. For
   each of the four cases below, what is the chance that the majority of coins
   will be tails when you are done?
   a. Two heads and three tails c. Four heads and one tail
   b. Three heads and two tails d. One head and four tails


7. For the following summations, give an equivalent equation without the
   summation:

a.

b.

c.

d.

e.

f.

() 3 i+ 7

i=1

N

∑

()i^2 – 2 i

i=1

N

∑

i

i=7

N

∑

() 2 i^2 + 1

i=5

N

∑

6 i

i=1

N

∑

4 i

i=7

N

∑