1
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Consider the following statements.

Statement (I): If E and F are two independent events, then $E^{\prime}$ and $F^{\prime}$ are also independent.

Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent.

Which of the following is correct?

A
Statement (I) is true and statement (II) is false
B
Statement (I) is false and statement (II) is true
C
Both the statements are true
D
Both the statements are false
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If A and B are two non-mutually exclusive events such that $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} \mid \mathrm{A})$, then

A
$\mathrm{A} \subset \mathrm{B}$ but $\mathrm{A} \neq \mathrm{B}$
B
$A=B$
C
$\mathrm{A} \cap \mathrm{B}=\phi$
D
$\mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})$
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?
A
$\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\frac{\mathrm{P}(\mathrm{B})}{\mathrm{P}(\mathrm{A})}$
B
$\mathrm{P}(\mathrm{A} \mid \mathrm{B})<\mathrm{P}(\mathrm{A})$
C
$\mathrm{P}(\mathrm{A} \mid \mathrm{B}) \geq \mathrm{P}(\mathrm{A})$
D
$\mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is $\frac{2}{5}$. If she visits temple $A, \frac{1}{3}$ is the probability that she meets her friend, whereas it is $\frac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her at temple B is

A
$\frac{7}{16}$
B
$\frac{5}{16}$
C
$\frac{3}{16}$
D
$\frac{9}{16}$
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