You have a bag of marbles with 600 marbles in it: 100 red, 240 green, and 260 blue. You pull out 1 marble, record the color, and replace it.

After you do this 150 times, the table shows the number of times each color was drawn:
\begin{tabular}{|c|c|c|c|}
\hline Red & Green & Blue & Total \\
\hline \hline 30 & 57 & 63 & 150 \\
\hline
\end{tabular}

Give exact, reduced answers.
a) What is the theoretical probability of drawing a blue?
b) What is the experimental probability of drawing a blue?

Step 1 ：We are given a bag of marbles with 600 marbles in it: 100 red, 240 green, and 260 blue. We pull out 1 marble, record the color, and replace it.

Step 2 ：We do this 150 times, and the table shows the number of times each color was drawn: 30 red, 57 green, and 63 blue.

Step 3 ：We are asked to find the theoretical and experimental probabilities of drawing a blue marble.

Step 4 ：The theoretical probability of drawing a blue marble is calculated by dividing the number of blue marbles by the total number of marbles. So, the theoretical probability is \(\frac{260}{600} = 0.43333333333333335\).

Step 5 ：The experimental probability of drawing a blue marble is calculated by dividing the number of times a blue marble was drawn by the total number of draws. So, the experimental probability is \(\frac{63}{150} = 0.42\).

Step 6 ：Final Answer: The theoretical probability of drawing a blue marble is approximately \(\boxed{0.433}\) and the experimental probability of drawing a blue marble is \(\boxed{0.42}\).