Probability Practice Test 2

For at least 3 trials, he has to fail at the first 2 attempts and then after that it does not make a difference if he fails or wins at the 3rd or the subsequent attempts.
Chance of success in any attempt $=\frac{1}{4}$
⇒ Chance of failure $=\frac{3}{4}$
⇒ Chance of failure in the first 2 attempts $={\left(\frac{3}{4}\right)}^2$
Chance of success at any attempt $=\frac{1}{4}$
⇒ Chance of failure $=\frac{3}{4}$
⇒ Chance of failure in the first 2 attempts $={\left(\frac{3}{4}\right)}^2=\frac{9}{16}$