Undergrad Probability Spaces | What You Need to Know

[WMDhamnekar]

TL;DR

Probability for firing shots independently and at random into the circular target with unit radius.

 

[PeroK]

The book answer to b) is correct. The probability that all five shots land in the outer part of the disk is $(\frac 3 4)^5$. And the probability that at least one lands in the inner disk is the complement of this.

 

[WMDhamnekar]

The book answer to b) is correct. The probability that all five shots land in the outer part of the disk is $(\frac 3 4)^5$. And the probability that at least one lands in the inner disk is the complement of this.

Please study the figure given below:

1, 3/4 1/2, 1/4 are the radii of the concerned concentric circles.

 

[PeroK]

Yes, I know. It's not to scale, but the answer remains $1- (\frac 3 4)^5$.