Probability Spaces | What You Need to Know

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SUMMARY

The discussion focuses on calculating probabilities within a defined probability space involving concentric circles. The probability that all five shots land in the outer part of the disk is established as \((\frac{3}{4})^5\). Consequently, the probability that at least one shot lands in the inner disk is determined to be the complement of this value, expressed as \(1 - (\frac{3}{4})^5\). The specific radii of the circles mentioned are 3/4, 1/2, and 1/4, which are critical for understanding the spatial distribution of the shots.

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WMDhamnekar
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TL;DR
Probability for firing shots independently and at random into the circular target with unit radius.
1664284103995.png
 
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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.
 
PeroK said:
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:

1664287749370.png
1, 3/4 1/2, 1/4 are the radii of the concerned concentric circles.
 
Yes, I know. It's not to scale, but the answer remains ##1- (\frac 3 4)^5##.
 
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