KCET2025MathematicsProbability
Consider the following statements. Statement (I): If E and F are two independent events, then E^ and F^ are also independent. Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent. Which of the following is correct?
Options
- AStatement (I) is true and statement (II) is false
- BStatement (I) is false and statement (II) is true
- CBoth the statements are true
- DBoth the statements are false
Correct answer
C. Both the statements are true
Step-by-step solution
E and F are two independent events, then E^ and F^ are also independent. Statement I true aligned & A ~B = P ( ~A ~B )=0 (1) & P ( ~A ) 0 (2) & P ( ~B ) 0 (3) aligned From eq(1), (2) and (3) P ( A B ) P ( A ) P ( B ) Statement II is true