Correct Answer - Option 4 :
\(\frac{11}{26}\)
Concept:
Conditional Probability:
The probability of an event occurring given that another event has already occurred is called a conditional probability.
- P(A ∩ B) = P(A) x P(B | A) = P(B) x P(A | B) where P(A | B) represents the conditional probability of A given B and P (A | B) represents the conditional probability of A given B.
Calculation:
Given: 2P(A) = P(B) = 5/13 and P(A | B) = 2/5
As we know that, P(A ∩ B) = P(A) x P(B | A) = P(B) x P(A | B)
\(⇒ \rm P(A | B) =\frac{P(A\cap B)}{P(B)}⇒ \frac{2}{5}=\frac{P(A\cap B)}{\frac{5}{13}}⇒ P(A\cap B)=\frac{2}{13} \)
∵ 2P(A) = 5/13 ⇒ P(A) =5/26
As we know that, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
\(\Rightarrow \rm P(A \cup B) =\frac{5}{26}+\frac{5}{13}-\frac{2}{13}⇒ P(A \cup B)=\frac{11}{26}\)
Hence, option 4 is the correct answer.
