# Probability question

##### New member
A cigarette company packs 1 to 5 different slips, labelled a, b, c, d, e, respectively with each pack it produces. Suppose that you buy 2 packs of cigarettes of this brand. What is a good sample space for the experiment whose outcome is the pair of slips you receive with 2 packs?

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#### Subhotosh Khan

##### Super Moderator
Staff member
Quen:A cigarette company packs 1 to 5 different slips, labelled a, b, c, d, e, respectively with each pack it produces. Suppose that you buy 2 packs of cigarettes of this brand. What is a good sample soace for the experiment whose outcome is the pair of slips you receive with 2 packs?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### pka

##### Elite Member
Quen:A cigarette company packs 1 to 5 different slips, labelled a, b, c, d, e, respectively with each pack it produces. Suppose that you buy 2 packs of cigarettes of this brand. What is a good sample soace for the experiment whose outcome is the pair of slips you receive with 2 packs?
HINT: If the set $$S=\{a,b,c,d,e\}$$ then $$S\times S=~?$$

#### Dr.Peterson

##### Elite Member
Quen:A cigarette company packs 1 to 5 different slips, labelled a, b, c, d, e, respectively with each pack it produces. Suppose that you buy 2 packs of cigarettes of this brand. What is a good sample soace for the experiment whose outcome is the pair of slips you receive with 2 packs?
What are all the possible pairs you could get? That list will be the sample space.

But I am confused by the mention of "1 to 5 different slips"; I suspect it really said, "1 OF 5 different slips", so that there is only one per pack.

##### New member
What are all the possible pairs you could get? That list will be the sample space.

But I am confused by the mention of "1 to 5 different slips"; I suspect it really said, "1 OF 5 different slips", so that there is only one per pack.
Ohh yes its "1of 5 different slips"...my mistake

#### Dr.Peterson

##### Elite Member
So, have you tried listing the sample space? It won't be very big. Once you try, we can either commend or correct you.

#### pka

##### Elite Member
$$\begin{array}{*{20}{c}}{(1,1)}&{(1,2)}&{(1,3)}&{(1,4)}&{(1,5)}\\{(2,1)}&{(2,2)}&{(2,3)}&{(2,4)}&{(2,5)}\\{(3,1)}&{(3,2)}&{(3,3)}&{(3,4)}&{(3,5)}\\{(4,1)}&{(4,2)}&{(4,3)}&{(4,4)}&{(4,5)}\\{(5,1)}&{(5,2)}&{(5,3)}&{(5,4)}&{(5,5)}\end{array}$$

##### New member
A cigarette company packs 1 to 5 different slips, labelled a, b, c, d, e, respectively with each pack it produces. Suppose that you buy 2 packs of cigarettes of this brand. What is a good sample space for the experiment whose outcome is the pair of slips you receive with 2 packs?
as order doesn't matter just list all possible pairs

{ (a,a) (a,b) (a,c) (a,d) (a,e) (b,b) (b,c) (b,d) (b,e) (c,c) (c,d) (c,e) (d,d) (d,e) (e,e) }

As order doesnt matter (b,a) and (a,b) are the same outcome so i think it will be correct answer.

##### New member
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

as order doesn't matter just list all possible pairs

{ (a,a) (a,b) (a,c) (a,d) (a,e) (b,b) (b,c) (b,d) (b,e) (c,c) (c,d) (c,e) (d,d) (d,e) (e,e) }

As order doesnt matter (b,a) and (a,b) are the same outcome so i think it will be answer.

#### Dr.Peterson

##### Elite Member
as order doesn't matter just list all possible pairs

{ (a,a) (a,b) (a,c) (a,d) (a,e) (b,b) (b,c) (b,d) (b,e) (c,c) (c,d) (c,e) (d,d) (d,e) (e,e) }

As order doesnt matter (b,a) and (a,b) are the same outcome so i think it will be correct answer.
Order doesn't matter in the statement of the problem; but you should also consider whether the outcomes you list are equally likely.

This may or may not be required in your definition of "sample space"; but it can make it easier to work with, so it may be taken into account in deciding whether your sample space is a "good" one. Is it?