Independence and the Multiplication Rule. Presentation 4.4 Overview and Examples. Independence. Two events are independent if knowing that one occurs does NOT change the probability that the other occurs. Examples
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Overview and Examples
Event A: Choosing a jack
P(A) = 4/52
Event B: Choosing a spade
P(B) = 13/52
If we simply added P(A) + P(B) to get 4/52 + 13/52 we would count the jack of spades TWICE!
These two events are NOT disjoint, since the jack of spades is an outcome in common!
Therefore use the general addition rule!
P(A or B) = P(A) + P(B) – P(A and B)
= 4/52 + 13/52 – 1/52
= 16/52 or .3077
Since the probability of getting a jack AND a spade is 1 out of 52 (since only one exists in the entire deck).