Michael is playing tournament chess against a computer program and the probability he wins against the program at any given game is 0.25. Find the probability that on the given day Nigel wins for the first time on the 4th game played.

1 answer

prob loses #1 = .75
prob loses #2 = .75 (2 lost in a row = .5625)
prob loses #3 = .75 (3 lost in a row = .421875)
prob then win #4 = .25*.421875 = 0.10546875