Answer:
Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], these two events are not independent.
Step-by-step explanation:
Independent events:
Two events, A and B, are independent if:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Event A: Male
Event B: Independent
Probability of male:
20 + 15 + 17 = 52 out of (20 + 15 + 17 + 18 + 12 + 7) = 89.
So
[tex]P(A) = \frac{52}{89}[/tex]
Probability of favoring independent:
20 + 18 = 38 out of 89. So
[tex]P(B) = \frac{38}{89}[/tex]
Probability of male and favoring independent:
20 out of 89. So
[tex]P(A \cap B) = \frac{20}{89}[/tex]
Test if they are independent:
[tex]P(A)P(B) = \frac{52}{89}*\frac{38}{89} = \frac{52*38}{89*89} = 0.24946[/tex]
[tex]P(A \cap B) = \frac{20}{89} = 0.22472[/tex]
Since [tex]P(A)P(B) \neq P(A \cap B)[/tex], these two events are not independent.
