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 information. We are given that events A and B are independent. We are given the probabilities: P(A) = 0.4 P(B) = 0.5 Step 2: Calculate the probabilities of the complements of events A and B. The probability of the complement of an event E, denoted P(E^c), is 1 - P(E). For event A: P(A^c) = 1 - P(A) = 1 - 0.4 = 0.6 For event B: P(B^c) = 1 - P(B) = 1 - 0.5 = 0.5 Step 3: Use the property of independent events. If events A and B are independent, then their complements A^c and B^c are also independent. For independent events E_1 and E_2, the probability of their intersection is P(E_1 E_2) = P(E_1)P(E_2). Therefore, for A^c and B^c: P(A^c B^c) = P(A^c)P(B^c) Step 4: Substitute the calculated values and find the result. P(A^c B^c) = (0.6)(0.5) P(A^c B^c) = 0.3 Step 5: Compare the result with the given options. The calculated value 0.3 matches option B. The final answer is B 3 done, 2 left today. You're making progress.