Two fair dice are rolled, and events A and B are as follows: Event A occurs if the largest number showing is at most 3. Event B occurs if neither 1 nor a 6 is showing Are they Independent?

I said that they are dependent because if Event A occurs where let's say a 1 occurs, then Event B does not occur. However, what happens when 2 occurs because then Event A occurs and Event B occurs as well.

  • $\begingroup$ Intuition is often reliable when it comes to dependence/independence. But not always, so I would advise calculating. $\endgroup$ Jun 16 '14 at 20:28
  • $\begingroup$ As @andrenicolas has suggest compute the probabilities, specifically the event space and see if the sets are independent I.e what values of the dies are permitted in the space for events A and then look at B. $\endgroup$
    – Chinny84
    Jun 16 '14 at 21:35

$A$ and $B$ are independent iff $$\Pr[A \cap B]=\Pr[A] \times \Pr[B],$$ where $\Pr[A \cap B]$ is the probability that both $A$ and $B$ occur simultaneously.

So, given this information, you tell me. Are $A$ and $B$ independent?

  • $\begingroup$ No they are not because the Prob(AnB) is 1/6 and the prob(A)*Prob(B) is .22222 $\endgroup$
    – user300
    Jun 16 '14 at 20:38

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