Probability to hit the target
= H= Probability to miss the target
= M= Required Probability that atleast 3 missile hit the target is
Here 1 – (P(x = 0) + P(x = 1) + P(x = 2)) ≥ 0.95
Here P(x = r) represents that r missile hits.
Here
1−(‌nC0()n+‌nC1() .()n−1+‌nC2()2.()n−2) ≥0.95 ∴
≤120 ...(1)
By putting different value of n.
We will get least value of n is 6.
For
n=5: L.H.S. of equation (1) is
=0.10703125 For
n=6: L.H.S. of equation (1) is
==0.037 Hence n = 6 missiles should be fired.