Correct Answer - Option 1 :
\(\frac{4}{5}\)
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: P(A) = 6/11, P(B) = 5/11 and P(A ∪ B) = 7/11
As we know that, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
So, by substituting the given values in the above formula we get,
\(\Rightarrow \rm \frac{7}{11}=\frac{6}{11}+\frac{5}{11}-P(A\cap B)\)
\(\Rightarrow \rm P(A\cap B)=\frac{4}{11}\)
As we know that, P(A ∩ B) = P(A) x P(B | A) = P(B) x P(A | B)
\(\Rightarrow \rm P(A | B) =\frac{P(A\cap B)}{P(B)}=\frac{\frac{4}{11}}{\frac{5}{11}}=\frac{4}{5}\)
Hence, option 1 is the correct answer.
