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Three sets are defined as A₁ = {1, 2, 3}, B = {1, 3, 4}, and C₁ = {2, 3, 4, 5}. Two elements are randomly selected without replacement from A₁, forming a subset T₁. Define A₂ as A₁ − T₁ and B₂ as B ∪ T₁. Next, two elements are randomly picked without replacement from B₂, forming a subset T₂. Define C₂ as C₁ ∪ T₂. Finally, two elements are randomly chosen without replacement from C₂, forming a subset T₃. Define A₃ as A₂ ∪ T₃. If it is given that A₁ equals A₃, let q represent the conditional probability of the event T₁ = {1, 2}. What is the value of q?
- 1/5
- 3/5
- 1/2
- 2/5
Correct answer: 1/5
Solution
The condition A₁ = A₃ imposes constraints on the subsets formed. Using probability rules and the given setup, the conditional probability q for T₁ = {1, 2} is calculated as 1/5.
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