2-15 (Review: Probability) Thomas has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For part below, if the marble selected is replaced before the next marble is drawn, find the probability for the draw. Write your answer as a fraction, as a decimal, and as a percent. a) A red marble? b) A red or a green marble? c) An orange marble?

To find the probabilities, we first need to determine the total number of marbles in the bag. Thomas has: - 7 green marbles - 5 blue marbles - 4 red marbles Total number of marbles = 7 (green) + 5 (blue) + 4 (red) = 16 marbles. Now, let's calculate the probabilities for each part: ### a) Probability of drawing a red marble The number of red marbles = 4. **Probability (P) of drawing a red marble:** \[ P(\text{red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{4}{16} = \frac{1}{4} \] **As a decimal:** \[ P(\text{red}) = 0.25 \] **As a percent:** \[ P(\text{red}) = 0.25 \times 100 = 25\% \] ### b) Probability of drawing a red or a green marble The number of green marbles = 7, and the number of red marbles = 4. **Total number of red or green marbles = 7 (green) + 4 (red) = 11.** **Probability (P) of drawing a red or green marble:** \[ P(\text{red or green}) = \frac{\text{Number of red or green marbles}}{\text{Total number of marbles}} = \frac{11}{16} \] **As a decimal:** \[ P(\text{red or green}) \approx 0.6875 \] **As a percent:** \[ P(\text{red or green}) \approx 0.6875 \times 100 \approx 68.75\% \] ### c) Probability of drawing an orange marble Since there are no orange marbles in the bag, the number of orange marbles = 0. **Probability (P) of drawing an orange marble:** \[ P(\text{orange}) = \frac{\text{Number of orange marbles}}{\text{Total number of marbles}} = \frac{0}{16} = 0 \] **As a decimal:** \[ P(\text{orange}) = 0 \] **As a percent:** \[ P(\text{orange}) = 0 \times 100 = 0\% \] ### Summary of Results: - a) Red marble: \(\frac{1}{4}\), 0.25, 25% - b) Red or green marble: \(\frac{11}{16}\), 0.6875, 68.75% - c) Orange marble: \(0\), \(0\), \(0\%\)