Test for proportion

#1
Hi.
Example 1:
Say I have a sample of rolls of a dice which may be 'uneven'
Say I have 10000 rolls, 1000 came up 1, 1000 came up 2, 2000 came up 3, 2000 came up 4, 2000 came up 5, 2000 came up 6.

Now I require some kind of test for the 'population' probability that each number comes up.

Example 2: One hundred tosses of a coin, 33 come up heads, 77 tails.
A test for the probability of obtaining a head?

Any help much appreciated. Cheers, ns
 
#2
I think your first step for both of these problems is to define your null and alternative hypotheses. For example, your first example has 6 different outcomes. i.e. there are six different probabilities that we are interrested in.

One null hypothesis we could test is:

Ho: p1 = p2 = p3 = p4 = p5 = p6

where p1 is the probability of observing a 1 on a given roll of the dice.

For the second example perhaps:

Ho: p(heads) = p(tails) = 0.5.

~Matt