(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?

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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