This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given probabilities. We are given the probabilities of events B_1, B_2, B_3 and the conditional probabilities of event A given B_1, B_2, B_3. P(B_1) = 0.2 P(B_2) = 0.3 P(B_3) = 0.5 P(A|B_1) = 0.1 P(A|B_2) = 0.4 P(A|B_3) = 0.8 Step 2: Apply the Law of Total Probability. Since B_1, B_2, and B_3 form a partition of the sample space, the probability of event A can be found using the Law of Total Probability: P(A) = P(A|B_1)P(B_1) + P(A|B_2)P(B_2) + P(A|B_3)P(B_3) Step 3: Substitute the given values into the formula. P(A) = (0.1)(0.2) + (0.4)(0.3) + (0.8)(0.5) Step 4: Compare with the given options. The expression derived matches option A. The final answer is A Send me the next one 📸