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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.
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Solution
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`
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