KCET 2025 | Probability Question 2 | Mathematics

A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then $\mathrm{P}(1$ or 3$)$ is

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{6}$

KCET 2025

MCQ (Single Correct Answer)

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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?

Statement (I) is true and statement (II) is false

Statement (I) is false and statement (II) is true

Both the statements are true

Both the statements are false

KCET 2025

MCQ (Single Correct Answer)

-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

$\mathrm{A} \subset \mathrm{B}$ but $\mathrm{A} \neq \mathrm{B}$

$A=B$

$\mathrm{A} \cap \mathrm{B}=\phi$

$\mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})$

KCET 2025

MCQ (Single Correct Answer)

-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?

$\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\frac{\mathrm{P}(\mathrm{B})}{\mathrm{P}(\mathrm{A})}$

$\mathrm{P}(\mathrm{A} \mid \mathrm{B})<\mathrm{P}(\mathrm{A})$

$\mathrm{P}(\mathrm{A} \mid \mathrm{B}) \geq \mathrm{P}(\mathrm{A})$

$\mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})$

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