Final answer:
In order to determine independence between pairs of events, compare the probability of their intersection to the product of their individual probabilities.
Step-by-step explanation:
In order for two events to be considered independent, the probability of both events occurring together, denoted as P(A ∩ B), must be equal to the product of the individual probabilities of each event, P(A) and P(B). Therefore, we can determine if the pairs of events are independent by comparing P(A ∩ B) to P(A)P(B).
Let's take a look at the given information:
- P(A) = 0.19
- P(B) = 0.10
- P(A ∩ B) = 0.06
To determine independence, we need to calculate P(A)P(B) and compare it to P(A ∩ B).
P(A)P(B) = (0.19)(0.10) = 0.019
Since P(A)P(B) is not equal to P(A ∩ B), the pairs of events A and B are not independent.