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3·2·1 = 2850120 Chapter 3 1 If A and B are independent events with P(A)=0 6 and P(B)=0 3, find the following: (a) P(A U B) (b) P(A n B) (c) P(A U B ) (d) P(AB)  



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(Note the use of the “independence of complements” property here ) 6 Given that A and B are independent with P(A ∪ B)=0 8 and P(B )=0 3, find P 



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2 2 Probability Reference List The following properties hold for all events A, B • P(∅) = 0 • 0 ≤ P(A) ≤ 1 • Complement: P(A)=1 − P(A) • Probability of a 



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2 Events A and B are said to be mutually exclusive iff Option 1 P(A B) = P(A) + P(A B)=0 ⇒ ∩ Q No 6 If A and B be two events such that P(A) = 0 6, P(B) 



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if the following statement is true: 4°N = B 410 4)X = 0 65 3 N6X = 13/0 Calc Tise 7 6 Let A and B be independent events, where P(A) = 0 6 and P(B) = x



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b) Calculate the probability of exactly one of the two events occurring (5) (2) 2 The independent events A and B are such that P(A) = 0 6, P(B) = 0 3 Find the - 0-72 b) P (AUB)_77 use a veni diagram Tip: Fill in the intersection x B first



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P(A∩B) = 0 27 ≠ 0 d Are A and B independent events? Why or why not? No P( BA) If P(W) = 0 6 and P(J) = 0 34 and P(JW) = 0 2, find the following: a P(W and J) = P(W ∩ J) 2 randomly selected mice are albino then brown? P(A ∩ B)  



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P[A/B] “ Probability of A given B “ ][ ][ ]/[ BP Events A and B are independent iff: not carry 9998 0 002 01][ 0002 0 5000 1 ][ = - = = = c HP HP 6 10*2



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P A P B P A B ∪ = + - ⋂ Mutually exclusive--Events A and B are mutually P A B P A P B ∪ = + 2 Example 1 The outcomes of two variables are 2 B 6 Conditional Probability To find the conditional probability that event A occur by the probability that B occurs Assumption: ( ) ( ) ( ) P A B P AB P B = ( ) 0

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