Alex flips a fair coin 20 times. Bert spins a fair coin 21
times. Bert wins if he gets more heads than Alex, else Alex wins.
Note that Alex wins if there is a tie. What is the probability that
Bert wins?

(In reply to

Solution by Gururaj)

Gururaj,

I agree with you...

I made up a full probability distribution table and the contrasted all possible outcomes.

The probability of any one outcome for Alex: 0.5^20

multiplied by the number of combinations of that many heads out of the 20 spins: (20 C x).

As for Bert: 0.5^21 and (21 C x).

It was then a matter of contrasting these against each other and summing for a total probablility of a win for each player.

The final answer... they both have a 0.5 chance of winning.