What is the probability that 4 depth charges will sink the submarine?

Q₄ = probability that 4 depth charges miss the submarine
$Q_4 = \left( \frac{1}{4} \right)^4$

$Q_4 = \frac{1}{256}$
 

Q₃ = probability that 3 depth charges miss the submarine and 1 damage
$Q_3 = \left( \frac{1}{4} \right)^3 \cdot \left( \frac{1}{4} \right)^1 \times {^4}C_3$

$Q_3 = \frac{1}{64}$
 

Q_escape = Probability that the submarine will escape in 4 depth charges
$Q_\text{escape} = Q_3 + Q_4$

$Q_\text{escape} = \frac{5}{256}$
 

P_sunk = Probability that 4 depth charges will sink the submarine
$P_\text{sunk} = 1 - Q_\text{escape}$

$P_\text{sunk} = \frac{251}{256}$   ←   answer