1. **Problem Statement:** You select a marble from a set of 8 marbles (7 pink and 1 purple) with replacement 8 times. We want to predict the expected number of times you will pick either a purple or a pink marble. 2. **Understanding the problem:** Since you replace the marble each time, the probability of picking any marble remains constant for each draw. 3. **Calculate probabilities:** - Probability of picking a pink marble $P(\text{pink}) = \frac{7}{8}$ - Probability of picking a purple marble $P(\text{purple}) = \frac{1}{8}$ 4. **Probability of picking pink or purple:** Since these are the only colors, the probability of picking either pink or purple is $$P(\text{pink or purple}) = P(\text{pink}) + P(\text{purple}) = \frac{7}{8} + \frac{1}{8} = 1$$ 5. **Expected value formula:** The expected number of times an event occurs in $n$ trials is $$E = n \times P(\text{event})$$ 6. **Apply the formula:** Here, $n=8$ trials and $P(\text{pink or purple})=1$, so $$E = 8 \times 1 = 8$$ 7. **Interpretation:** Since every marble is either pink or purple, you will always pick a pink or purple marble every time. So the best prediction is that you will pick a pink or purple marble all 8 times. **Final answer:** The best prediction for the number of times you will pick a purple or pink marble in 8 draws with replacement is **8**.