Respuesta :
Answer:
Event A and B are independent
Step-by-step explanation:
Events A and B are independent if and only if
[tex]P(A \cap B) = P(A) \cdot P(B)[/tex]
As per the statement:
The probability of event A is 0.65 and the probability of event B is 0.76.
⇒[tex]P(A) = 0.65[/tex] and  [tex]P(B) = 0.76[/tex]
It is also given that the probability of both event A and event B occurring is 0.494.
[tex]P(A \cap B) =0.494[/tex]
Find: [tex]P(A \cap B)[/tex]
[tex]P(A) \cdot P(B) = 0.65 \cdot 0.76[/tex]
Simplify:
[tex]P(A \cap B) = 0.494[/tex]
⇒[tex]P(A) \cdot P(B) =P(A \cap B)[/tex]
therefore, Events A and B are independent.
