# Probability Spaces | What You Need to Know

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• WMDhamnekar
In summary, the book answer for part b) is correct. The probability that all five shots land in the outer part of the disk is ##(\frac 3 4)^5##. The probability that at least one shot lands in the inner disk is the complement of this, which is ##1- (\frac 3 4)^5##. The figure provided shows the radii of the concentric circles, although it is not to scale.
WMDhamnekar
MHB
TL;DR Summary
Probability for firing shots independently and at random into the circular target with unit radius.

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:

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##.

WMDhamnekar

## 1. What is a probability space?

A probability space is a mathematical concept used to model random events or experiments. It consists of three components: a sample space, an event space, and a probability function.

## 2. How is a sample space defined?

A sample space is a set that contains all possible outcomes of an experiment. It is usually denoted by the symbol Ω and can be finite, countably infinite, or uncountably infinite.

## 3. What is an event space?

An event space is a collection of subsets of the sample space that represent different events or outcomes of an experiment. It is denoted by the symbol ℱ and can contain singletons, unions, intersections, and complements of events.

## 4. How is probability defined in a probability space?

Probability is a numerical measure of the likelihood of an event occurring in a probability space. It is defined as a function P that maps events to real numbers between 0 and 1, where 0 represents impossibility and 1 represents certainty.

## 5. What are some real-life applications of probability spaces?

Probability spaces are used in various fields such as statistics, finance, physics, and engineering to model and analyze random phenomena. Some examples include predicting stock market trends, designing reliable computer networks, and understanding the behavior of subatomic particles.

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