and B
. How do you mathematically determine whether events A
and B
are independent?(1 point)
Responses
P(A and B)=P(A)P(B)
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
P(A and B)=P(A)−P(B)
upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis minus upper P left parenthesis upper B right parenthesis
P(A and B)=P(A)+P(B)
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
P(A and B)=P(A)⋅P(B)
1 answer
To determine whether events A and B are independent, you use the following mathematical condition:
\[ P(A \text{ and } B) = P(A) \cdot P(B) \]
This means that the probability of both events A and B occurring together is equal to the product of their individual probabilities.
So, the correct response from your options is:
P(A and B) = P(A)P(B)
