What is the probability of getting a heads on a coin and then getting a 5 on a number cube?

In probability theory, sample space (also called sample description space[1] or possibility space[2]) of an experiment or random trial is the set of all possible outcomes or results of that experiment.[3] A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols. They can also be finite, countably infinite, or uncountably infinite.[4]

For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}, commonly written {H, T}.[5] For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}, commonly written {HH, HT, TH, TT}.[6] If the sample space is unordered, it becomes {{head,head}, {head,tail}, {tail,tail}}.

For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).[7]

A subset of the sample space is an event, denoted by E. Referring to the experiment of tossing the coin, the possible events include E={H} and E={T}.[6]

A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).

Another way to look at a sample space is visually. The sample space is typically represented by a rectangle, and the outcomes of the sample space denoted by points within the rectangle. The events are represented by ovals, and the points enclosed within the oval make up the event.[8]

a

step-by-step explanation:

rurbrbrjrnrbjr

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560