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Which pairs of events are independent? (a) P(A)=0.19,P(B)=0.10,P(A∩B)=0.06.

User Alcamtar
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1 Answer

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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.

User Goosebumps
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