Question

Which statement is true about whether A and B are independent events? A and B are independent events because P(A∣B) = P(A) = 0.12. A and B are independent events because P(A∣B) = P(A) = 0.25. A and B are not independent events because P(A∣B) = 0.12 and P(A) = 0.25. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25

Answer 1

Answer:The answer is D

Step-by-step explanation:

Answer 2

The events A and B are independent if the  probability that event A occurs does not affect the probability that event B occurs.
A and B are independent if the equation P(A∩B) = P(A) P(B) holds true.
P(A∩B) is the probability that both event A and B occur.
Conditional probability is the probability of an event given that some other event first occurs.
P(B|A)=P(A∩B)/P(A)
In the case where events A and B are independent the conditional probability of event B given event A is simply the probability of event B, that is P(B).
Statement 1:A and B are independent events because P(A∣B) = P(A) = 0.12. This is true.
Statement 2:A and B are independent events because P(A∣B) = P(A) = 0.25.
This is true.
 Statement 3:A and B are not independent events because P(A∣B) = 0.12 and P(A) = 0.25. 
This is true.
Statement 4:A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25
This is true.