The question is incomplete. Here is the complete question:
Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.95 probability that he will hit it. One day, Samir decides to attempt to hit 10 such targets in a row.
Assuming that Samir is equally likely to hit each of the 10 targets, what is the probability that he will miss at least one of them?
Answer:
40.13%
Step-by-step explanation:
Let 'A' be the event of not missing a target in 10 attempts.
Therefore, the complement of event 'A' is ![\overline A=\textrm{Missing a target at least once}](https://tex.z-dn.net/?f=%5Coverline%20A%3D%5Ctextrm%7BMissing%20a%20target%20at%20least%20once%7D)
Now, Samir is equally likely to hit each of the 10 targets. Therefore, probability of hitting each target each time is same and equal to 0.95.
Now, ![P(A)=0.95^{10}=0.5987](https://tex.z-dn.net/?f=P%28A%29%3D0.95%5E%7B10%7D%3D0.5987)
We know that the sum of probability of an event and its complement is 1.
So, ![P(A)+P(\overline A)=1\\\\P(\overline A)=1-P(A)\\\\P(\overline A)=1-0.5987\\\\P(\overline A)=0.4013=40.13\%](https://tex.z-dn.net/?f=P%28A%29%2BP%28%5Coverline%20A%29%3D1%5C%5C%5C%5CP%28%5Coverline%20A%29%3D1-P%28A%29%5C%5C%5C%5CP%28%5Coverline%20A%29%3D1-0.5987%5C%5C%5C%5CP%28%5Coverline%20A%29%3D0.4013%3D40.13%5C%25)
Therefore, the probability of missing a target at least once in 10 attempts is 40.13%.