THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The joint probabilities shown in a table with two rows,A₁ and A₂,and two columns,B₁ and B₂ are as follows: P(A₁ ∩ B₁) = 0.10,P(A₁ ∩ B₂) = 0.30,P(A₂ ∩ B₁) = 0.05,P(A₂ ∩ B₂) = 0.55
-What is P(A₂ |B₂) ,rounded to two decimals?

Question

Quizplus · Accepted Answer

Using Bayes' theorem: P(A₂ | B₂) = P(B₂ | A₂) * P(A₂) / P(B₂) We know: P(B₂ | A₂) = 0.55, P(A₂) = 0.60, and P(B₂) = P(B₂ | A₁) * P(A₁) + P(B₂ | A₂) * P(A₂) = 0.30 * 0.40 + 0.55 * 0.60 = 0.46 Therefore, P(A₂ | B₂) = 0.55 * 0.60 / 0.46 = 0.65 (rounded to two decimals).