A police-man fires four bullets on a dacoit. The probability that the dacoit will be killed by one bullet is 0.6. What is the probability that the dacoit is still alive?

Let A_i ; i = 1,2,3,4 be the event that the dacoit is not killed by the i^th bullet, 

Then, P(Ai) = 1 – 0.6 = 0.4

Now, Probability that the dacoit is still alive

= P (A₁ ∩ A₂ ∩ A₃ ∩ A₄) P (A₁) P (A₂) P (A₃) P (A₄)

[Since all 4 shots are independent]

= (0.4)⁴ = 0.0256