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Consider events A and B. Suppose the following:

$\text{P(event A and not B)} = 0.12$
$\text{P(event B and not A)} = 0.22$
$\text{P(events A and B)} = 0.18$

Are events A and B independent?

A

It is clear that events A and B are not independent since $\text{P(A and B)}$ is greater than zero.

B

Events A and B are independent since at least one of them must occur.

C

Events A and B are not independent since $0.12+0.22+0.18$ is not equal to $1$, or $100\%$.

D

Events A and B are not independent since ($0.3\cdot 0.4$) is not equal to $0.18$.

E

Events A and B are not independent since ($0.12\cdot0.22$) is not equal to $0.18$.

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