Theoretical vs Experimental Probability of Drawing Marbles

Published on April 18, 2026

Statistics

Calculate the theoretical probability using the marble counts and the experimental probability from the observed draws with replacement.

Question

Here’s how to solve the problem step-by-step:

Part a) Theoretical Probability of Drawing a Blue Marble

Identify the total number of marbles: The problem states there are 600 marbles in the bag.
Identify the number of blue marbles: The problem states there are 280 blue marbles.
Calculate the theoretical probability: The theoretical probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
Reduce the fraction: Divide both the numerator and the denominator by their greatest common divisor.
- Divide by 10:
- Divide by 4:

Part b) Experimental Probability of Drawing a Blue Marble

Identify the total number of trials: The problem states that you pull out a marble 100 times.
Identify the number of times a blue marble was drawn: The table shows that blue marbles were drawn 45 times.
Calculate the experimental probability: The experimental probability is the ratio of the number of times an event occurred to the total number of trials.
Reduce the fraction: Divide both the numerator and the denominator by their greatest common divisor.
- Divide by 5:

Answers:

a) The theoretical probability of drawing a blue marble is

b) The experimental probability of drawing a blue marble is