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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