\begin{tabular}{|l|l}\hline A jar contains 30 red marbles, 12 yellow marbles, 8 green \\ marbles and 5 blue marbles \end{tabular}\( \quad \begin{array}{r}\text { 19. What is the probability that you draw and } \\ \text { replace marbles } 3 \text { times and you get NO } \\ \text { red marbles? (answer in } 3 \text { decimals) }\end{array} \)

To find the probability of drawing no red marbles when drawing and replacing marbles 3 times, we need to calculate the probability of not drawing a red marble in each draw and then multiply these probabilities together. Given: - Total number of marbles = 30 red + 12 yellow + 8 green + 5 blue = 55 marbles - Number of non-red marbles = 12 yellow + 8 green + 5 blue = 25 marbles The probability of not drawing a red marble in one draw is the number of non-red marbles divided by the total number of marbles: \[ P(\text{not red}) = \frac{25}{55} \] Since we are drawing and replacing marbles 3 times, we need to calculate the probability of not drawing a red marble in each draw and then multiply these probabilities together: \[ P(\text{no red in 3 draws}) = \left(\frac{25}{55}\right)^3 \] Now, we can calculate this probability. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{25}{55}\right)^{3}\) - step1: Reduce the fraction: \(\left(\frac{5}{11}\right)^{3}\) - step2: Use the properties of exponents: \(\frac{5^{3}}{11^{3}}\) - step3: Evaluate the power: \(\frac{125}{11^{3}}\) - step4: Evaluate the power: \(\frac{125}{1331}\) The probability of drawing no red marbles when drawing and replacing marbles 3 times is approximately 0.0939.