Question
For two events A and B , if P ( A )= P ( A B )= 1 4 and P ( B A )= 1 2 , then which of the following is not true?
BITSAT
Mathematics
Probability
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. A and B are independent
- B. P ( A ^ B )= 3 4
- C. P ( B ^ A ^ )= 1 2
- D. None of these
Answer
D. None of these
Step-by-step solution
P ( B A )= 1 2 P ( B A ) P ( A ) = 1 2 P ( B A )= 1 8 P ( A B )= 1 4 P ( A B ) P ( B ) = 1 4 P ( B )= 1 2 P ( A B )= 1 8 = P ( A ) P ( B ) Events A and B are independent. Now, P ( A ^ B )= P ( A B ) P ( B ) = P ( A ) P ( B ) P ( B ) = 3 4 and P ( B ^ A ^ )= P ( B ^ A ^ ) P ( A ^ ) = P ( B ^ ) P ( A ^ ) P ( A ^ ) = 1 2
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