Answer:
No
Step-by-step explanation:
We know that
any two events are mutually exclusive when
P(A or B)=P(A)+P(B)
we are given
P(A or B)[tex]=\frac{2}{7}[/tex]
[tex]P(A)=\frac{1}{3}[/tex]
[tex]P(B)=\frac{1}{7}[/tex]
we can add P(A)+P(B)
[tex]P(A)+P(B)=\frac{1}{3}+\frac{1}{7}[/tex]
now, we can simplify it
[tex]P(A)+P(B)=\frac{1\times 7}{3\times 7}+\frac{1\times 3}{7\times 3}[/tex]
[tex]P(A)+P(B)=\frac{7+3}{3\times 7}[/tex]
[tex]P(A)+P(B)=\frac{10}{21}[/tex]
we can see that it is not equal to 2/7
so, A and B are not mutually exclusive
so,
No
