The solutions are [tex]{P}({A} \text { and }B})=0[/tex] and [tex]P}({A} \text { or } {B})=\frac{7}{12}[/tex]
Explanation:
Given that the sets A and B are independent events and are mutually exclusive events.
We need to determine the value of [tex]P(A \text { and } B)[/tex] and [tex]P(A \text { or } B)[/tex]
The value of [tex]P(A \text { and } B)[/tex]:
Since, the sets A and B are mutually exclusive events, it is impossible for the two events to occur together.
Hence, we have,
[tex]{P}({A} \text { and }B})=0[/tex]
Thus, the value of [tex]P(A \text { and } B)[/tex] is 0.
The value of [tex]P(A \text { or } B)[/tex]:
For mutually exclusive events, the value of [tex]P(A \text { or } B)[/tex] is given by the formula,
[tex]P(A \text { or } B)=P(A)+P(B)[/tex]
Substituting the values, we get,
[tex]P(A \text { or } B)=\frac{1}{4}+\frac{1}{3}[/tex]
[tex]P}({A} \text { or } {B})=\frac{7}{12}[/tex]
Hence, the value of [tex]P(A \text { or } B)[/tex] is [tex]\frac{7}{12}[/tex]
Thus, the solutions are [tex]{P}({A} \text { and }B})=0[/tex] and [tex]P}({A} \text { or } {B})=\frac{7}{12}[/tex]
