Question

\use the Venn diagram to calculate probabilities.

Answer 1

Answer: The first and the third.

The two statements that are correct are the first and third options. 

In the first choice, we are looking for values that are in A given that they are already a part of B. 14 of the values in B are also in A. This can be reduced to 2/3 as shown.

In the third choice, we are simply looking for the fraction of the entire chart that are in A. There are 31 values in A and 59 in the total chart. Therefore, the fraction 31/59 is correct.

Answer 2

Answer : 1 and 3 are the correct probabilities.

→According to the given Venn diagram.

Total number of elements  = 59.

1)P(C)=$\frac{21}{59}$ and $P(A\cap C)=\frac{14}{59}$ then

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

2)P(B)=$\frac{27}{59}$ and  $P(C\cap B)=\frac{11}{59}$ then

$P(C|B)=\frac{P(C\cap B)}{P(B)}$$=\frac{\frac{11}{59}}{\frac{27}{59}}=\frac{11}{27}$$\neq \frac{8}{27}$

3) P(A) =$\frac{number\ of\ elements\ in\ A}{Total\ elements}=\frac{31}{59}$

4) P(C) =$\frac{number\ of\ elements\ in\ C}{Total\ elements}=\frac{21}{59}$$\neq \frac{3}{7}$

5) $P(B|A)=\frac{P(B\cap A)}{P(A)}$$=\frac{\frac{13}{59}}{\frac{31}{59}}=\frac{13}{31}$$\neq \frac{13}{27}$

Therefore, option 1 and 3 are correct.