Probability and Events

Question

Event A is "roll 4 on a dice" and event B is "roll a 2 on a die."

Are the events dependent or independent, and why?

Answers:

Events A and B are dependent, because P(A) does not equal P(B|A)

Events A and B are independent, because P(A)=P(B|A)=1/36

Events A and B are independent, because P(B)=P(B|A)=1/6

Answer 1

These are dependent, but the first choice doesn't give the correct reason. If you want to conclude independence/dependence by comparing probabilities, you compare P(A) to P(A|B). In this case, the former probability is 1/6, while the latter is 0 (because you can't roll both a 4 and a 2 with one die roll).

Answer 2

This is badly worded.....We do not determine independence by calculating probabilities!!

Independence is determined simply by the logic of the situation. With something like rolling dice, flipping coins, etc. each action stands on it's own---it does not change the boundary conditions for the next action.

By contrast, if you draw a card from a standard deck, the probability of the next draw is affected--because there are now fewer cards.