Year 12s: what will be the first way you research your future options? >>

Venn diagram probability

Tabath

Last part is causing a problem. Either its being marked wrong or I'm making a mistake. Anyone see it?

Reply 1

mqb2766

How did you come up with that?
What did you from the individual probabilities?

(edited 4 years ago)

Reply 2

Tabath

4/70 is p(picking pupil who plays all 3 sports) and 49/69 is P(picking pupil who plays only one sport)

Multiply those probabilities together and cancel down

Reply 3

mqb2766

Those are correct, but you must have made a mistake cancelling. There is an obvious common factor of 14 (not 6).

Original post by Tabath

4/70 is p(picking pupil who plays all 3 sports) and 49/69 is P(picking pupil who plays only one sport)

Multiply those probabilities together and cancel down

(edited 4 years ago)

Reply 4

Tabath

Ok so that gives P(3 sports)=1/14 multiplied by p(only 1 sport)=49/69 giving 7/138 after cancelling down?

Problem is its marking that wrong as well so must have made another arithmetic error but I can't see it

Reply 5

mqb2766

That is still not cancelling right. 4/70 cancels to 2/35.

In
4*49/(70*69)
there is a factor of 14

Original post by Tabath

Reply 6

Tabath

Yeah, whichever way its cancelled it gets down to 14/345 which is being marked wrong? Maybe theres a bug in the marking because I don't think my method is wrong?

Reply 7

mqb2766

14/345 is what I get. Is this really wrong?

Original post by Tabath

Yeah, whichever way its cancelled it gets down to 14/345 which is being marked wrong? Maybe theres a bug in the marking because I don't think my method is wrong?

Reply 8

Tabath

Thats what I got, I think there must be a bug in the marking system. I just wanted to check I hadn't made any silly arithmetic mistakes as I'm sure my method is correct.

Its conditional probability so the denominator of 2nd event goes from 70 to 69. But as first event(playing all 3 sports) doesn't effect the 2nd event(play only 1 sport) the total for the numerator stays the same.

Reply 9

mqb2766

The only thing I could think is that the denom would be 70^2 which would simplify to 1/25.

Reply 10

Tabath

Original post by mqb2766

The only thing I could think is that the denom would be 70^2 which would simplify to 1/25.

No, denominator is definately 70x69. I did try 70x70 just in case but it also marked that wrong and that would not be conditional probability anyway.

Reply 11

mqb2766

II'm being dumb :-)
The group is not ordered so it should be double that. Draw the tree and you see there are two probabilities that need to be added together A,B and B,A.

Reply 12

Tabath

Ah yes, DUH! I didn't even think to draw a tree as I didn't need to for the other parts!! Thanks very much

Reply 13

mqb2766

Using a coin analogy, the other questions were H,H or T,T type occurences, whereas this is H,T OR T,H.
Fairly common question type, I should have twigged it earlier.

Original post by Tabath

Ah yes, DUH! I didn't even think to draw a tree as I didn't need to for the other parts!! Thanks very much