Hi.

You need to sum all possible events like

prob("first-try password is correct") = 1/4

prob("sencond-try password is correct") = prob(first-try password was wrong)*prob("secondt-try password is correct") = 3/4 * 1/3

(there are 4 passwords, 3 of them are wrong: so 3/4 - after that try there are 3 passwords remaining, two of them are incorrect, 1 of them is correct => 1/3 )

prob("last-try password is correct") = prob("fail, fail, correct") 3/4*2/3*1/2

prob("she types in the correct password before getting banned") = 1/4+3/4*1/3 + 3/4*2/3*1/2 = 0.75 = 75% = prob("not getting banned")

Rapha