Question

Evaluate P(A ∪ B), if 2P(A) = P(B) = $\frac{5}{13}$ and P(A|B) = $\frac{2}{5}$

Answer 1

Answer:

$\frac{11}{26}$

Step-by-step explanation:

Concept:

Addition theorem of probabaility:

P(A∪B) = P(A)+P(B)-P(A∩B)

Given:

$2 P(A) = P(B) = \frac{5}{13}$

$P(A)=\frac{5}{26}\\\\P(B) =\frac{5}{13}$

Now,

P(A|B)=$\frac{2}{5}$

P(A∩B)/P(B)=$\frac{2}{5}$

P(A∩B)=$\frac{2}{5}.\frac{5}{13}$

P(A∩B)=$\frac{2}{13}$

P(A∪B) = P(A)+P(B)-P(A∩B)

P(A∪B) = $\frac{5}{26}+\frac{5}{13}-\frac{2}{13}$

P(A∪B) =$\frac{5+10-4}{26}$

P(A∪B) =$\frac{11}{26}$