One final question on the reading problem

venda

Dave

Posers and Puzzles

05 Apr 21

venda

Dave

S.Yorks.England

Joined: 18 Apr 10
Moves: 87107

05 Apr 21

I think I have got the necessary formula in a spreadsheet now so if you could indulge me (just one more time hopefully!! ) ,I have tried some random numbers in it:-
If there are 30 people in the class and the set is a b c d e f what is the probability that 4 pupils read set a b e and f?
My spreadsheet says 9%
Is this right?

~~Removed~~

Joined: 10 Dec 06
Moves: 8528

05 Apr 21

@venda said
I think I have got the necessary formula in a spreadsheet now so if you could indulge me (just one more time hopefully!! ) ,I have tried some random numbers in it:-
If there are 30 people in the class and the set is a b c d e f what is the probability that 4 pupils read set a b e and f?
My spreadsheet says 9%
Is this right?

Ok, so now there is 6 books to choose from, and they are instructed to choose 4 of them to read.

so a,b,e,f is 1 of C(6,4) = 15

With 30 students having exactly 4 of them read the desired subset there are

C( 30,4 ) ways to select students to read that set and the remaining 26 students have 14 subsets to choose from

There are C( 30,4)*14^( 30-4 ) ways to do this.

The total number of ways for 30 students to select any subset to read is:

15^30

Thus, the probability of exactly 4 of them reading the subset a,b,e,f is given by ( assuming all subsets are equally likely to be chosen ):

P( exactly 4 read books a,b,e,f ) = C( 30,4)*14^( 30-4 )/15^30 ≈ 9%

Good Job Venda!

venda

Dave

S.Yorks.England

Joined: 18 Apr 10
Moves: 87107

06 Apr 21

@joe-shmo said
Ok, so now there is 6 books to choose from, and they are instructed to choose 4 of them to read.

so a,b,e,f is 1 of C(6,4) = 15

With 30 students having exactly 4 of them read the desired subset there are

C( 30,4 ) ways to select students to read that set and the remaining 26 students have 14 subsets to choose from

There are C( 30,4)*14^( 30-4 ) ways to ...[text shortened]... ):

P( exactly 4 read books a,b,e,f ) = C( 30,4)*14^( 30-4 )/15^30 ≈ 9%

Good Job Venda!

Thanks Joe.
Now I have the method (I used bigdoggs formula)I can now tidy up my spreadsheet a bit so for any similar type problems I can just plug in the numbers and it'll give me the answer.