Question

Use the Venn diagram to calculate probabilities.

Answer 1

1. The number of elements of the universal set, or the sample space is 59

2. P(A|C) is the probability of A to happen once we know C has occured

it is calculated using the formula P(A|C) = P(A ∩ C) / P(C) = (14/59)/(21/59)=14/21=2/3

3. P(C|B) = P(C ∩ B) / P(B) = (11/59)/(27/59)=11/27

4. P(C)=(6+8+3+4)/59=21/59

5. P(B|A) = P(B ∩ A) / P(A) = (13/59)/(31/59)=13/31

Correct answer: P(A|C) = 2/3

Answer 2

Total number of elements in the set =59.

1)P(A|C) = P(A ∩ C) / P(C)  = $\frac{14}{21}=\frac{2}{3}$

2)P(C|B) = P(C ∩ B) / P(B) =$\frac{11}{27}$

3) P(A) =$\frac{31}{59}.$

4)P(C) =$\frac{21}{59}.$

5)P(B|A)=P(B ∩ A) / P(A)=$\frac{13}{31}$

Options 1 and 3  are right.