# Question -Sample space in probability

• MHB
• lola19991
In summary, the sample space for this experiment is the set of all possible sequences of numbers 1, 2, 3, 4, 5, 6 where 6 is the last number. The event En represents throwing the dice n times, with n-1 combinations of numbers 1-5 followed by a 6. The total number of sequences for n-1 combinations is 5^(n-1).
lola19991
I would like to know how to solve the following question:
Throw a cube until you get the number 6, then stop throwing.
a) What is the sample space of the experiment?
b) Let's call the event to throw the cube n times En. How much elements from the sample space are within En?
**The cube is a standard six-sided die, with the numbers "1" thru "6" printed on the sides**

lola19991 said:
I would like to know how to solve the following question:
Throw a cube until you get the number 6, then stop throwing.
a) What is the sample space of the experiment?
b) Let's call the event to throw the cube n times En. How much elements from the sample space are within En?
**The cube is a standard six-sided die, with the numbers "1" thru "6" printed on the sides**

Hi! What have you tried so far?

I'm sure you're capable of solving part a)! Remember, the sample space is the set of all possible outcomes for a random experiment. Can you list all the possible outcomes of throwing a die (exclude any exceptional cases)?

Joppy said:
Hi! What have you tried so far?

I'm sure you're capable of solving part a)! Remember, the sample space is the set of all possible outcomes for a random experiment. Can you list all the possible outcomes of throwing a die (exclude any exceptional cases)?

I know that the possible outcomes of throwing a die is: {1, 2, 3, 4, 5, 6}. I don't know how to start solving this problem because I've just started studying, so
I don't know how to begin...

The "sample space" is the set of all things that can happen. Here, where you are throwing a six sided die until you get a 6, the sample space is the set of all sequence of numbers 1, 2, 3, 4, 5, 6 which have 6 as the last number but no where else. "2, 3, 1, 5, 1, 3, 4, 6" is in the sample space. "1, 3, 2, 1, 4, 5" is not because it does not end in "6". "3, 5, 3, 4, 6, 2, 1, 3, 6" is not because there is a "6" that is not the last number in the sequence.

In event "En", throwing the dice n times, there must be the numbers "1, 2, 3, 4, 5" n-1 times followed by a 6. In how many ways can you have n-1 different combinations of those 5 numbers?

Here are some easy examples: if n= 1, n- 1= 0 and the only possible sequence is "6", 1 sequence.

If n= 2, n- 1= 1 and we can have only "16", "26", "36", "46" and "56", 5 sequences.

If n= 3, n- 1= 2 and we can have only "116", "126", "136", "146", "156", "216", "226", "236", "246", "256", "316", "326", "336", "346", "356", "416", "426" "436", "446", "456", "516", "526", "536", "546" and "556". How many are there? Do you get the idea?

## What is a sample space in probability?

A sample space in probability is the set of all possible outcomes of an experiment or a random phenomenon. It is denoted by the symbol "S" and is the foundation of probability theory.

## How is a sample space represented?

A sample space can be represented in several ways, depending on the experiment or scenario. It can be shown using a list, a table, a tree diagram, or a Venn diagram.

## What is the importance of a sample space in probability?

A sample space helps us to understand the possible outcomes of an experiment and calculate the probability of each outcome occurring. It also allows us to determine the total number of possible outcomes, which is essential in many probability calculations.

## What are the elements of a sample space?

The elements of a sample space are the individual outcomes that make up the set. They can be numbers, letters, symbols, or words, depending on the experiment. Each element represents a unique outcome of the experiment.

## How is a sample space related to events in probability?

A sample space and events in probability are closely related. An event is a subset of the sample space, meaning it is a collection of one or more outcomes from the sample space. The probability of an event is calculated by dividing the number of outcomes in the event by the total number of outcomes in the sample space.

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