Answer:
A) Not mutually exclusive
Step-by-step explanation:
Given
[tex]P(A) = \frac{1}{4}[/tex]
[tex]P(B) = \frac{3}{5}[/tex]
[tex]P(A\ or\ B) = \frac{7}{10}[/tex]
Required
Determine if they are mutually exclusive or not
Mutually exclusive are defined by:
[tex]P(A\ or\ B) = P(A) + P(B)[/tex]
So, we have:
[tex]P(A\ or\ B) = \frac{1}{4} + \frac{3}{5}[/tex]
Take LCM
[tex]P(A\ or\ B) = \frac{5+12}{20}[/tex]
[tex]P(A\ or\ B) = \frac{17}{20}[/tex]
By comparing:
[tex]P(A\ or\ B) = \frac{17}{20}[/tex] ---- Calculated
[tex]P(A\ or\ B) = \frac{7}{10}[/tex] ---- Given
We can conclude that A and B are not mutually exclusive because:
[tex]\frac{17}{20} \ne \frac{7}{10}[/tex]
