Final answer:
The theoretical probability of drawing a red marble from the jar is 32% or 0.32, calculated by dividing the number of red marbles by the total number of marbles in the jar.
Step-by-step explanation:
The question is asking for the theoretical probability of drawing a red marble from a jar containing a total of 100 marbles of various colors. To calculate this probability, you divide the number of red marbles by the total number of marbles. So, with 32 red marbles and a total of 100 marbles (30 green, 23 orange, 32 red, and 15 brown), the probability would be:
Probability of drawing a red marble = Number of red marbles / Total number of marbles
Probability of drawing a red marble = 32 / (30 + 23 + 32 + 15)
Probability of drawing a red marble = 32 / 100
Probability of drawing a red marble = 0.32 or 32%
This means that the theoretical probability of drawing a red marble is 32% or as a decimal, 0.32.