MHB Question -Sample space in probability

[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 E_n?
**The cube is a standard six-sided die, with the numbers "1" thru "6" printed on the sides**

 

[Joppy]

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 E_n?
**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)?

 

[lola19991]

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...

 

[HallsofIvy]

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?