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
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Independence and the Multiplication Rule
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).