Question

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.

Answer 1

Let r = no of bombs hit the target

p=0.8

q=0.2            (1-p=q)

n=10            r=4

`p(r=4)=""^nC_rp^rq^(n-r)`      r=0,1,2...........,n

`=""^10C_4(0.8)^4(0.2)^6`

`=""^10C_4(8/10)^4(2/10)^6`

`=(10!)/(4!6!) xx(2)^18(1/10)^10`

`=(10xx9xx8xx7)/(4xx3xx2)xx(2)^18xx(1/10)^10`

`=210xx(2)^18xx(1/10)^10`

`=(262144xx210)/(10)^10=55050240/(10)^10`

`=Anti[log210+18log2-10]`

`=Anti[2.3222+18log(0.3010)-10]`

`=Anti(3.7402)`

`=0.0055`