1. **State the problem:** We have two bags with marbles of different colors and quantities. - Bag A: 4 white, 4 purple - Bag B: 10 white, 6 purple We want to order these events from least likely to most likely: Event 1: Choosing a white marble from Bag A. Event 2: Choosing a white or purple marble from Bag A. Event 3: Choosing an orange marble from Bag B. Event 4: Choosing a purple marble from Bag B. 2. **Calculate probabilities:** - Probability of Event 1 (white from Bag A): $$P_1 = \frac{4}{4+4} = \frac{4}{8} = \frac{1}{2} = 0.5$$ - Probability of Event 2 (white or purple from Bag A): Since Bag A only has white and purple marbles, this is certain: $$P_2 = 1$$ - Probability of Event 3 (orange from Bag B): There are no orange marbles in Bag B, so: $$P_3 = 0$$ - Probability of Event 4 (purple from Bag B): $$P_4 = \frac{6}{10+6} = \frac{6}{16} = \frac{3}{8} = 0.375$$ 3. **Order events from least to most likely:** $$P_3 = 0 < P_4 = 0.375 < P_1 = 0.5 < P_2 = 1$$ 4. **Final answer:** Least likely ----------------------------- Most likely Event [3], Event [4], Event [1], Event [2] This means choosing an orange marble from Bag B is impossible (least likely), then choosing purple from Bag B, then white from Bag A, and finally choosing any marble from Bag A (white or purple) is certain (most likely).