Responses
Show that P(A and B)=P(B)P(A).
Show that upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction upper P left parenthesis upper B right parenthesis over upper P left parenthesis upper A right parenthesis End Fraction .
Show that P(A and B)=P(A)⋅P(B).
Show that upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis .
Show that P(A and B)=P(A)+P(B).
Show that upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis plus upper P left parenthesis upper B right parenthesis .
Show that P(A and B)=P(A)P(B).
Show that upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction upper P left parenthesis upper A right parenthesis over upper P left parenthesis upper B right parenthesis End Fraction .
1 answer
To determine if the outcome of two events \( A \) and \( B \) is independent, you can use the following criterion:
Show that \( P(A \text{ and } B) = P(A) \cdot P(B) \).
This means that if the probability of both events happening together (\( P(A \text{ and } B) \)) is equal to the product of their individual probabilities (\( P(A) \) and \( P(B) \)), then the events are independent.
So the correct response is:
Show that \( P(A \text{ and } B) = P(A) \cdot P(B) \).
