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Help- Venn diagrams

In a group of 31 students, 7 study both Art and Biology.
14 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Reply 1

Ash-M :)

Original post by Keira444

7 study both Art and Biology.

?

Just do 7/31 and that's the probability, I guess.

Reply 2

Pangol

Original post by Ash-M :)

?

Just do 7/31 and that's the probability, I guess.

This doesn't take into account the bit that says "Given that a randomly selected student studies Art".

Questions like this are usually very easy once the Venn diagram has been drawn. Is there any help needed with that part?

Reply 3

Ash-M :)

Original post by Pangol

Oops your right, I didn't see that bit. In that case P(Art n Bio) I P(A)
So use the conditional probability formula:
P(Art n Bio) / P(A)

Reply 4

Ash-M :)

Original post by Ash-M :)

Oops your right, I didn't see that bit. In that case P(Art n Bio) I P(A)
So use the conditional probability formula:
P(Art n Bio) / P(A)

The probability of Art and Biology divided by the probability of just Art

Reply 5

Pangol

Since this has been tagged as GCSE level, I doubt that use of the conditional probability formula is required.

OP - start with your Venn diagram. Do you need any help with that?