StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q4E

Expert-verifiedFound in: Page 452

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

**Question: Show condition ** ${\mathbf{\left(}}{\mathit{i}}{\mathbf{\right)}}$ **and ** ${\mathbf{\left(}}{\mathit{i}}{\mathit{i}}{\mathbf{\right)}}$ **are met under Laplace's definition of probability, when outcomes are equally likely.**

**Answer**

** **

Condition $\left(i\right)$ and $\left(ii\right)$ are met under Laplace's definition of probability when outcomes are equally likely.

** **

Let $S$ be the sample space of an experiment with a finite or countable number of outcomes. $P\left(s\right)$ Be the probability of each outcome $S$ .

Condition :

$0\u2a7dP\left(s\right)\u2a7d1$ For each $s\in S.$

This states that the probability of each outcome is non negative real number which is no greater than .

Condition $\left(ii\right)$ :

$\sum _{s\in S}P\left(s\right)=1$

This states that the sum of all probabilities of all possible outcome should be $1$ .

** **

**Generalization of Laplace's definition in which each ${\mathbf{n}}$** ** outcomes is assigned a probability of $\frac{\mathbf{1}}{\mathbf{n}}$** **.**

** **

The conditions$\left(i\right)$ and $\left(ii\right)$ are satisfied when the Laplace's definition of the probability of equally likely outcomes is used and $S$ is finite.

Hence, when there are possible outcomes ${x}_{1},{x}_{2},{x}_{n}$ the two conditions are to be satisfied.

$0\u2a7dP\left(s\right)\u2a7d1\text{for}i=1,2,\dots \dots \dots ...n\phantom{\rule{0ex}{0ex}}\sum _{i=1}^{n}P\left({x}_{J}\right)=1$

The function from the set of all outcomes of the sample space $S$ is called the probability distribution. Conditions $\left(i\right)$ and $\left(ii\right)$ are met under Laplace's definition of probability when outcomes are equally likely.

94% of StudySmarter users get better grades.

Sign up for free