Answer:
[tex](B) P(B)=\dfrac{16}{31}[/tex]
Step-by-step explanation:
From the Venn diagram, n(AUB)=31
The given probabilities in the option are calculated below:
[tex]P(A)=\dfrac{21}{31}\\\\P(B)=\dfrac{16}{31}\\\\P(A|B)=\dfrac{P(A\cap B)}{P(B)}= \dfrac{6/31}{16/31} =\dfrac{6}{16}=\dfrac{3}{8} \\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{6/31}{21/31} =\dfrac{6}{21}=\dfrac{3}{7}[/tex]
The only correct option is the probability of B which is [tex]\frac{16}{31}[/tex]
