Question

Use the Venn diagram to calculate probabilities

Which probability is correct?


P(A) = 3/5

P(B) = 16/31

P(A|B) = 2/7

P(B|A) = 10/21

Answer 1

The answer is 3/5

21/35=3/5=P(A)

A is the correct answer

Answer 2

From the Venn diagram, we can gather that there are 35 total objects (6 in both A and B; 15 in A but not B; 10 in B but not A; and 4 in neither A nor B), and we have the probabilities

`\mathbb P(A\cap B)=\frac6{35}`

`\mathbb P(A)=(15+6)/(35)=(21)/(35)=\frac35` (this is the answer)

`\mathbb P(B)=(10+6)/(35)=(16)/(35)`

By definition of conditional probability,

`P(A\mid B)=(P(A\cap B))/(P(B))=\frac{\frac6{35}}{(16)/(35)}=\frac6{16}=\frac38`

`P(B\mid A)=(P(B\cap A))/(P(A))=\frac{\frac6{35}}{(21)/(35)}=\frac6{21}=\frac27`