Probability
Conditional probability of events
nta_pyq_2025_apr
Grade 12
Question:
If A and B are two events such that P$(A) = 0.7$,$P(B) = 0.4$and P(A$\cap$$B) = 0.5$, where B denotes the ¯ ¯¯¯ ¯ ¯¯¯ complement of B, then P (B | (A$\cup$B)) ¯ is equal:-
Step-by-Step Solution
Key Concept: Compute the favourable cases for conditional probability of events and divide by the total equally likely cases.
$P(A) = 7$,$P(B) = 4$10 10 (1) 5 ¯ ¯¯¯ P(A$\cup$$B) = 10$¯ ¯¯¯ B P(B$\cap$(A$\cup$B)) P( ) = ¯ ¯¯¯ ¯ ¯¯¯ A$\cup$B P(A$\cup$B) ¯ ¯¯¯ P((B$\cap$B)$\cup$(B$\cap$A)) P(A$\cap$B) = = ¯ ¯¯¯ ¯ ¯¯¯ P(A$\cup$B) P(A$\cup$B) ¯ ¯¯¯ 7 5$P(A) - P(A$$\cap$$B) - 10$10 = = ¯ ¯¯¯ ¯ ¯¯¯ 7 4 5$P(A) + P(B) - P(A$$\cap$$B) + (1 - ) - 10$10 10 2 1 = = 8 4
Correct Answer: 1