Probability Spaces | What You Need to Know

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Discussion Overview

The discussion revolves around the calculation of probabilities related to shots landing in different areas of a disk, specifically focusing on the probability that at least one shot lands in the inner disk versus all shots landing in the outer part. The context appears to be homework-related, involving mathematical reasoning and probability theory.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • Some participants assert that the book's answer is correct, stating that the probability of all five shots landing in the outer part of the disk is ##(\frac 3 4)^5##.
  • Others reiterate that the probability of at least one shot landing in the inner disk is the complement of the probability that all shots land in the outer disk.
  • A participant acknowledges that the figure provided is not to scale but maintains that the probability remains ##1 - (\frac 3 4)^5##.

Areas of Agreement / Disagreement

Participants generally agree on the calculation of the probabilities, but there is a lack of consensus on the implications of the figure's scale and its relevance to the problem.

Contextual Notes

The discussion does not clarify the assumptions regarding the scale of the figure or how it may affect the interpretation of the probabilities.

WMDhamnekar
MHB
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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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