Question

Sets A and B are independent events and are mutually exclusive

Answer 1

The solutions are ${P}({A} \text { and }B})=0$ and $P}({A} \text { or } {B})=\frac{7}{12}$

Explanation:

Given that the sets A and B are independent events and are mutually exclusive events.

We need to determine the value of $P(A \text { and } B)$ and $P(A \text { or } B)$

The value of $P(A \text { and } B)$:

Since, the sets A and B are mutually exclusive events, it is impossible for the two events to occur together.

Hence, we have,

${P}({A} \text { and }B})=0$

Thus, the value of $P(A \text { and } B)$ is 0.

The value of $P(A \text { or } B)$:

For mutually exclusive events, the value of $P(A \text { or } B)$ is given by the formula,

$P(A \text { or } B)=P(A)+P(B)$

Substituting the values, we get,

$P(A \text { or } B)=\frac{1}{4}+\frac{1}{3}$

$P}({A} \text { or } {B})=\frac{7}{12}$

Hence, the value of $P(A \text { or } B)$ is $\frac{7}{12}$

Thus, the solutions are ${P}({A} \text { and }B})=0$ and $P}({A} \text { or } {B})=\frac{7}{12}$