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by: Grace Heavey

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# Math 130 Statistics 130L

Grace Heavey

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Notes for 4.4
COURSE
Statistics 130L
PROF.
Dr. Sebesta
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Math

This 2 page Class Notes was uploaded by Grace Heavey on Monday October 10, 2016. The Class Notes belongs to Statistics 130L at Marist College taught by Dr. Sebesta in Fall 2016. Since its upload, it has received 4 views. For similar materials see Statistics 130L in Math at Marist College.

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Date Created: 10/10/16
Intro to Statistics 4.4 Probability & The Multiplication Rule Chapter 4 begins our discussion of probability. In section 1 &2 we learned the basics of probability and in section 3 we learned the addition rule. This section continues our discussion of probability with the multiplication rule,used when you want to ﬁnd the probability of Event A AND Event B happening. 4.3 Multiplication Rule: Notation: P(A and B) - probability that eventA occurs on the ﬁrst trial and event B occurs on the second trial P(B|A) - probability of event B givenA probability that event B happens given that eventA already occurred Formal Multiplication Rule P(A and B)= P(A)-P(B|A) Intuitive Multiplication Rule: To ﬁnd the probability of event a and event b multiply the probability of event a by the probability of event b taking into consideration that event a already happened independent: the probability of event a doesn't affect the probability of event b ex:coin toss,rolling a single die,pulling one card and replace it dependent: the occurrence of event a affects the probability of event b ex:bag of marbles,2 blue,3 red and don't replace P(Blue and Red)= 2/5 x 3/4 = 6/20 P(Blue) = 2/5 P(Red) = 3/4 Sampling with replacement: when you return“eventA” back to sample pool Sampling without replacement: when you do not return“eventA” back to sample pool ▯1 Examples: With Replacement: draw a card from a deck of 52 P( queen and red) P(queen)=4/52 P(red)=26/52 P(queen and red)= (4/52)x (26/52)= 104/2704=.0385 Without Replacement: draw a card from deck of 52 P(queen and red) P(queen)= 4/52 P(red)= 26/51 (26/51)x(4/52)= 104/2652= .0392 Why the Multiplication RuleWorks: Quiz 1. T/F 2. multiple choice 5 choices P(both correct) P(T/F) = 1/2 P(multiple choice) = 1/5 (1/2)x(1/5)= 1/10 TA,TB,TC,TD,TE FA,FB,FC,FD,FE 10 sample choices 1 correct answer 1/10 ▯2

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