Geometric Distribution

Suppose we wanted to know the chances of flipping a coin and only seeing a head by the fourth flip, how can we find this?

We can use the geometric distribution which calculates the probability of the number of failures before a success in a Bernouli trail.

The formula is

p(x) = (1-p)^xp, where x = 0,1,2,...

Where p(x) is the number of failures, or for our example, the number of tails.

So to apply the formula, what are the chances of flipping a head for the first time on the 4th toss? (This means flipping 3 tails first)

p(x) = number of failures before flipping a head (3)

p(3) = (1 - 0.5)³(0.5) = 0.0625 or around 6%

Pretty low odds!