Assume that when you play a game you win with probability p

Assume that when you play a game, you win with probability p = 0.55, and lose with probability 1 p = 0.45. What is the probability that after playing 10 games the number of your victories is the same as the number of your losses?

Solution

After 10 games we need the 5 victories and 5 losses

Thus, the required probability

=  ¹⁰C₅ p⁵ (1-p)⁵

= ¹⁰C₅ (0.55)⁵ (0.45)⁵

= 0.2340

Hope this helps,