All of the choices are correct, therefore the correct option is d.
Given:
The given sets are:
[tex]S=\{1,2,3,4,5,6\}[/tex]
[tex]A=\{1,2\}[/tex]
[tex]B=\{3,4\}[/tex]
To find:
The correct statement for the given sets.
Explanation:
Two sets are mutually exclusive if they have no common elements.
Clearly, the set A and set B have no common elements. So, A and B are mutually exclusive. The union of set A and set B is:
[tex]A\text{ or }B=\{1,2,3,4\}[/tex]
Now,
[tex]n(A\text{ or }B)=4[/tex]
[tex]n(S)=6[/tex]
[tex]P(A\text{ or }B)=\dfrac{n(A\text{ or }B)}{n(S)}[/tex]
[tex]P(A\text{ or }B)=\dfrac{4}{6}[/tex]
And,
[tex]P(A)+P(B)=\dfrac{2}{6}+\dfrac{2}{6}[/tex]
[tex]P(A)+P(B)=\dfrac{2+2}{6}[/tex]
[tex]P(A)+P(B)=\dfrac{4}{6}[/tex]
[tex]P(A)+P(B)=P(A\text{ or }B)[/tex]
Since all of the choices are correct, therefore the correct option is d.
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