Probability Question

ninebeanrows

This has just really made me go insane for the last few minutes.

Okay here we go.

In an English Exam, 4 out of 8 poets appear on the paper. What is the probability of a student who studies 3 poets, having one of these three poets appearing on the day.
for the exam.

If you want a guarantee you should study 5 poets

I forget the actual probability actually...

Fuzzy_Dunlop

Nothing to see here

Edit- Sorry i believe i just calculated the odds for if all 3 were to come up. I'm confused

Hagar

That doesn't sound right.
If he only studied one poet the odds would be 8 to 1. of getting a poet he knew.
If three are studied the odds must be less than 8 to 1.
Probably about 5 to 2 roughly.

Fuzzy_Dunlop

Hagar wrote:

That doesn't sound right.
If he only studied one poet the odds would be 8 to 1. of getting a poet he knew.
If three are studied the odds must be less than 8 to 1.
Probably about 5 to 2 roughly.

Oh sweet jesus i'm retarded, feckin probability.

cold_filter

Hagar wrote:

That doesn't sound right.
If he only studied one poet the odds would be 8 to 1. of getting a poet he knew.
If three are studied the odds must be less than 8 to 1.
Probably about 5 to 2 roughly.

Yes but its the probability of him picking the correct ones i.e. poet B , Poet Z poet Z as a random rather than picking poet a,b,c.

i think!!

cocoa

Hagar wrote:

If he only studied one poet the odds would be 8 to 1. of getting a poet he knew.

no, because there's four poets out of the eight on the paper, the odds are 1 in 2 if you have one poet.

with two poets, it's 11/14 (~79%)

three poets: 13/14 (~93%)

4 poets : 69/70 (~99%)

you should be able to guess the rest...

of course, all of these probabilites are assuming one poet is as likely as another which isn't technically true so...

[I used combinations, you split the eight into the # studied and the number # not studied. Then pick the four not on the exam with the # studied among them, divide by the total number of outcomes (8nCr4)Then take your answer away from one to get the probability of all poets studied not not being on the exam. for 1 poet this is {1nCr1 * 7nCr3}/8nCr4=35/70=1/2 ]

ninebeanrows

79% if you do 2 poets? thats gotta be wrong ?

thanks for the attempts!

I am looking for the maths bit! I'm doing 5 well 4 but abit of a 5th one.

A Primal Nut

Im a bit rusty but I think:

Probability of exactly 4 out of 5 poets not studied chosen from 8

(5C4*3C0) /(8C4)
= 5C4/8C4

Therefore probabilty of at least one poet studied been chosen:
Ans = 1 - (5C4/8C4)

Edit: 5C4 = 5!/4! = 5,
8C4 = 8!/(4!*4!) = 40320/576 = 70

Therefore
Ans = 1 - (5/70) = 65/70 = 92.86%

Seems quite high, but same answer as cocoa.

A Primal Nut

Hagar wrote:

That doesn't sound right.
If he only studied one poet the odds would be 8 to 1. of getting a poet he knew.

There is four poets coming up on the paper so the odds is better than 8 to 1, more like 2 to 1. That explains why all these answers are higher than expected.

Weathercheck wrote:

79% if you do 2 poets? thats gotta be wrong ?

thanks for the attempts!

I am looking for the maths bit! I'm doing 5 well 4 but abit of a 5th one.

Edit for mistake:
Im getting somewhere around the same for two poets ie 1-(6C4/8C4)=(55/70).

Does seem quite high but bear in mind you only need one of those two poets to come up, and half the 8 poets are coming up on the paper so there is a good chance at least one will come up. Dossers rejoice!

Formula in case you want to change number of poets studied would be:

1- [((8-x)C4)/(8C4)]

Where x is the number of poets studied.

cocoa

Weathercheck wrote:

79% if you do 2 poets? thats gotta be wrong ?

no, you just don't realise how bad (as odds go) that is...

For example, approx 50000 people do the leaving every year, if hypothetically, they all did only four poets (not the same four) then 500 of them would be left unable to answer. If they only did two then 10500 of them would be unable to answer...

of course, I say it again, these odds are based on the idea that each poet is as probable as the next which is almost certainly untrue.

sunflowerz

study the 2 female poets ....a female poet always comes up

OR

study the 3 irish poets......an irish poet always comes up

but always is such a strong word, they'd probably change everything this year just to screw with our heads though a little bit

I'm studying 5 just to be on the safe side