Question

the probability of hitting a target in any shot is 0.2 if 5 shots are fired find the probability that the target will be hit at least twise​

Answer 1

P (hitting target) = 0.2 = 2/10 = 1/5

This means that, P(not hitting target) = 4/5 = 0.8

Therefore, we can say that from the 5 shots fired 1 will hit, while 4 shots fired will not.

So the probability of target hit once = the probability of hitting target one-time × (the probability of not hitting a target 4 times) = (0.2)×(0.8)^4

And the probability of target never hit = 0.8^5

So now,

The probability of the target hit twice will be = 1 - target hit once - target hit never

= 1 - [0.2×(0.8^4)]−0.8^5

Here taking 0.8^4 common, we get

1 - (0.8^4)(0.2 + 0.8)

= 1 - (0.8^4)(1) = 1 - (0.8^4)

= 1 - 0.4096

= 0.5904

I think this should be the correct answer.