Hawkeye Foodlemyer is firing a rifle at a paper target 500m away. The target is 10cm square, and each bullet hole is circular, 1cm in diameter. The bullet holes are uniformly distributed in the target area, and none extend beyond the boundary. (A) How many bullets must be fired before there is a 50% chance that 2 bullet holes overlap? (B) How many bullets must be fired before there is a 50% chance that the next bullet hole will overlap an existing hole?

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gaurav4067
Profile Answers by gaurav4067

Dec 5th, 2010

Target 500m away not used in soln. (I guess given unnecessarily)
we make holes on the target area , we get 10*10 = 100 holes on the sheet
now we take one shot, and let say it hits any one hole.

Now the probability of hitting the same hole in first try=1/100
2 shots: 99/100*1/00
similarly in nth shot = 99/100^(n-1)*1/100

Sum of all probabilities => hitting the same hole in n tries after the first
shot..
= 1/100(1+99/100+99/100^2 + .......n terms ) = 1/2 (given)
we solve for n we get around 70 tries ( so 70+1(first shot) ..=71 shots