Question 994671: a soldier hits her target with a probability of 3/10. How many times should she shoot at the target to ensure at least 70% chance of hitting the target?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! You want 0.7, the probability of missing, to be raised to the x power to where it is less than 0.3, for at that point, there will be a greater than 70% chance of hitting the target.
0.7^x=0.3
ln both sides
x ln(.7)=ln(.3)
-0.357x= -1.204
x is greater than 3 but less than 4. Therefore, she has to shoot 4 times.
0.7^4=0.2401, and the probability of 4 misses in a row is 76%, and the probability of hitting the target is at least 70%.
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