Question

Use the Venn diagram to calculate probabilities.

Answer 1

Corrected Question

These are the given probabilities. The Venn diagram is also attached. are (A) P(A|C) = 2/3

(B) P(C|B) = 8/27

(C) P(A) = 31/59

(D) P(C) = 3/7

(E) P(B|A) = 13/27

Answer:

A and C

Step-by-step explanation:

$P(A|C)=\dfrac{P(A\cap C)}{P(C)}= \dfrac{14/59}{21/59}=\dfrac{14}{21}=\dfrac{2}{3}$

$P(C|B) =\dfrac{P(C\cap B)}{P(B)}= \dfrac{11/59}{27/59}=\dfrac{11}{27}\neq \dfrac{8}{27}\\\\P(A) = \dfrac{31}{59}\\\\P(C) =\dfrac{21}{59}\neq \dfrac{3}{7}\\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{13/59}{31/59}=\dfrac{13}{31}\neq\dfrac{13}{27}$

From the above, only A and C are correct.