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A rifleman is firing at a distance targe...

A rifleman is firing at a distance target and hence has only 10% chance of hitting it. Find the number of rounds; he must fire in order to have more than 50% chance of hitting it at least once.

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Let a rifieman fires n number of rounds.
Probability of hitting the targeet, `p=1/10.`
`therefore` Probability of not hitting the target, `q=1-1/10=9/10.`
`therefore` Probability of hitting the target at least once `=1-((9)/(10))^(n)`
Given that `1-((9)/(10))^(n)gt1/2`
`therefore((9)/(10))lt1/2`
So, the least value of n is 7.
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