Spinning off this debate;
What is the chance of getting 5 of each when flipping a coin? Im pretty sure its rare? Although it should be the norm?
Im all question marks, so have at it.
The odds are (5!*5!)/10!)/10^2 =252/1024= about 24.6%
5! means 1*2*3*4*5, there are 252 paths to get 5 spins of each from 1024 total paths.
Note I accidentally transposed the expression, it should be (10!/(5!*5!))/10^2
You transposed the bottom, too: 2^10, not 10^2.
My post from another thread may be helpful as well:
If you want a reasonably simple method to calculate other heads/tails results:
If you flip n coins, expand (H+T)^n. If you want to know the probability of x heads and n-x tails, look for the H^x T^(n-x) in your expansion. Isolate it, plug in your probabilities for both H and T (50% of each if they are fair coins (and by the way, all the coins need to have the same bias for this method to work: For example if one coin is biased 70% H, 30% T, then all coins must have that same probability)) and the result is the probability you want.
For example, with three coins: (H+T)^3 = H^3 + 3H^2 T + 3H T^2 + T^3. Assuming the coins are all fair, the probability of flipping 2 heads, 1 tail would be 3H^2 T = 3(.5)^2 (.5) = 37.5%.
The graph shown here shows the probability of each number of heads, from 0 to 10: