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Probability

You have a fair 6 sided die and are asked to calculate the probability of getting an even or a prime. How do I work this out without actually listing all the possibilities and adding them. Can this be illustrated on a Venn diagram and I have to use an equation?
Thanks
Favourable outcomes are 2,3,4,5,6
All outcomes are 1,2,3,4,5,6

seems simple to find the probability by listing

you can use a venn diagram too
then P(even U prime) = P(even) + P(prime) - P(prime and even)
Original post by BobbJo
Favourable outcomes are 2,3,4,5,6
All outcomes are 1,2,3,4,5,6

seems simple to find the probability by listing

you can use a venn diagram too
then P(even U prime) = P(even) + P(prime) - P(prime and even)


But if I do that I get 3/6 + 3/6 -9/36 =3/4 which is incorrect. How do I work out the correct P(PnE)?
Original post by Y12_FurtherMaths
But if I do that I get 3/6 + 3/6 -9/36 =3/4 which is incorrect. How do I work out the correct P(PnE)?

P(even) x P(prime) ≠ \neq P(even and prime)
[only true if the 2 events are independent, which is not the case]

P(Prime n Even) = n(Prime n Even)/n(Sample space)
set of Prime n Even = {2}
sample space = {1,2,3,4,5,6}
so P(Prime n Even} = 1/6
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Avatar for Notnek
Notnek
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Original post by Y12_FurtherMaths
You have a fair 6 sided die and are asked to calculate the probability of getting an even or a prime. How do I work this out without actually listing all the possibilities and adding them. Can this be illustrated on a Venn diagram and I have to use an equation?
Thanks

Are you aware that just considering each number (i.e. listing) is the quickest way to do this and that it's a KS3 level question? Are you just curious about other methods?
Original post by Notnek
Are you aware that just considering each number (i.e. listing) is the quickest way of doing this? Are you just curious about other methods?


I am aware but if I get asked a different type of question listing all the possibilities isn’t the most efficient way of doing it and I want to know how to actually do it
Original post by Y12_FurtherMaths
I am aware but if I get asked a different type of question listing all the possibilities isn’t the most efficient way of doing it and I want to know how to actually do it

listing all the possibilties is usually a very good and reliable method
Original post by BobbJo
listing all the possibilties is usually a very good and reliable method

Ok thank you for your help. Just to check is the P(EnP) = 1/6 and they are not independent events?
Original post by Y12_FurtherMaths
Ok thank you for your help. Just to check is the P(EnP) = 1/6 and they are not independent events?

yes
Original post by BobbJo
yes


Cheers

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