In a throw of two dice , what is the probability of gatting a 7 or 11 ?

Explanation

Let A be the event of throwing a 7 and B be the event of throwing (65) or (56) for a total of 11
Since these event are mutually exclusive ` P(Z uu B) = P(A) P(B) = (6)/(36) + (2)/(36) = (8)/(36)`
In conditional probability , the sample space is reducced to the set B rather thatn the set of all out
comes , and the favorable outcomes are those in both A and B ` (AnnB)= P(A |B)` is the probability
that A occurs given that B occurred . This results in the formula ` P (A|B) = (P(Ann B))/(P(B)) ` .
Multiplying both sides of this equation by P(B) produces the equivalent formula ` P(A nn B) = `
P(B) P(A)b) . If the probability of event A occurring does not depend on whether event B occurs.
then A and B are said to be indepancent P(A|B) = P(A) . thus , if A and B are indepandent
event ,` P(Ann B) = (P(B) . P(A)` .