(a) Consider the tree in Fig 4b, Section 2 2 Are the events A on the second day, the price is larger than 9 , B on the second day, the price is smaller than 12 independent (b) In general, if 1 , 2 , 3 , 4 with given elementary probabilities, in which case are the events A 1 , 2 , 3 and B 2 , 3 , 4 independent 10 2 3 1 3 14 FIGURE 4 8 2 5 3 5 4 5 1 5 (b) 15 Probability (2 3)(2 5) 4 15 11 Probability (2 3)(3 5) 6 15 10 Probability (1 3)(4 5) 4 15 5 Probability (1 3)(1 5) 1 15

Question: (a) Consider the tree in Fig. 4b, Section 2.2. Are the events A={on the second day, the price is larger than 9}, B = {on

(a) Consider the tree in Fig. 4b, Section 2.2. Are the events A={on the second day, the price is larger than 9}, B = {on the second day, the price is smaller than 12} independent?

(b) In general, if Ω = {ω₁, ω₂, ω₃, ω₄} with given elementary probabilities, in which case are the events A = {ω₁, ω₂, ω₃} and B = {ω₂, ω₃, ω₄} independent? 10 2/3 1/3 14 FIGURE 4. 8 2/5 3/5 4/5 1/5 (b) 15 Probability-(2/3)(2/5)-4/15 11 Probability=(2/3)(3/5)=6/15

10 2/3 1/3 14 FIGURE 4. 8 2/5 3/5 4/5 1/5 (b) 15 Probability-(2/3)(2/5)-4/15 11 Probability=(2/3)(3/5)=6/15 10 Probability=(1/3)(4/5)=4/15 5 Probability=(1/3)(1/5)=1/15

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