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

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

$\mathbb P(A\cap B)=\dfrac6{35}$

$\mathbb P(A)=\dfrac{15+6}{35}=\dfrac{21}{35}=\dfrac35$ (this is the answer)

$\mathbb P(B)=\dfrac{10+6}{35}=\dfrac{16}{35}$

By definition of conditional probability,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\frac6{35}}{\frac{16}{35}}=\dfrac6{16}=\dfrac38$

$P(B\mid A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\frac6{35}}{\frac{21}{35}}=\dfrac6{21}=\dfrac27$

Answer 2

The answer is 3/5

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

A is the correct answer