If you flip a coin 100 times how many times will it land on heads?

[nmanlamb]

1. The problem statement, all variables and given/known data
If you flip 1 quarter 100 times what are the odds all 100 flips would land heads?
My friend argues that it would be a 50% chance since each individual flip has a 50% chance of being heads.

2. Relevant equations



3. The attempt at a solution
I tried saying that its 50% chance per flip but it decreases by (0.50) ^ x each flip. x being the number of flips. Is there anyone out there who can help me explain this to him? His platform is that flipping 1 coin 100 times is different from flipping 100 coins 1 time. The probability of each should be the same though right?

[LCKurtz]

You are correct. It is $\frac 1 {2^{100}}$, very very small. Have your friend try it for just 5 in a row and he will soon see it isn't 1/2 even for that.

[Ray Vickson]

Your are right: the probability of getting 100 heads in 100 tosses is about 0.79x10^(-30), or 0.000 ..... 00079 (with 30 0s after the decimal point). If your friend still wants to argue the point, try to explain it with the easier case of tossing 2 times instead of 100. Now there are four possible outcomes, and it is easy enough to list them all. Only one of those four has two 'heads'. If your friend STILL wants to argue the point, ask him what he thinks are the probabilities of each of the four outcomes.

RGV

[genericusrnme]

you are correct

You could try getting him to write our every possible configuration you could end up with after 100 coin tosses, then asking him (or his ancestors via a message passed down since both of you would be dead by the time it's dnoe) how many out of the 2^100 configurations has all tails