What is a countably infinite sample space?

A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers. Countably infinite is in contrast to uncountable, which describes a set that is so large, it cannot be counted even if we kept counting forever. …

Can a sample space have infinite outcomes?

A sample space is a collection of all possible outcomes of a random experiment. Later on we shall introduce probability functions on the sample spaces. A sample space may be finite or infinite. Infinite sample spaces may be discrete or continuous.

Can an infinity be the probability?

In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed (i.i.d.) random variables.

What is the probability of an impossible?

0
The probability of an impossible event is 0.

How do you find the probability of a sample space?

There isn’t a set formula for finding the sample space unless you are given (or can solve for) the probability and specific event values. You then use the formula P = Specific Event / Sample Space, plug in the P and SE values, and cross multiply to find the SS.

Who said there exist sets which have over countably infinitely many elements?

Cantor
History. In 1874, in his first set theory article, Cantor proved that the set of real numbers is uncountable, thus showing that not all infinite sets are countable. In 1878, he used one-to-one correspondences to define and compare cardinalities.

Which of the following refers to a sample space that is finite or countably infinite?

An event is a subspace of the sample space of a random experiment. A sample space is discrete if it consists of a finite (or countably infinite) set of outcomes.

When an event is impossible to happen its probability is?

What is the Probability of an Impossible Event? The probability of an impossible event is 0. Impossible events can’t occur.

Does anything have a probability of 0?

Every point has zero probability but every point can be a possible outcome. Similarly, in a 2-dimensional space, a line also has zero probability. In other words, only events that have a significant enough likelihood can have positive probability in a continuous space.

What is the probability of an impossible null event?

The probability of an impossible event is always 0 as for an impossible event, E = 0 and thus, P(E) = 0.

What is the probability of an impossible even and a sure event?

For example ,it’s a sure event to obtain a number between 1 and 6 when rolling an ordinary die. The probability of a sure event has the value of 1. The probability of an impossible event has the value of 0.