Question

Erik is performing a marble experiment in math class. His teacher places an equal number of black, red, and white marbles in a bag. Then, Erik randomly takes out a marble, records the result, and puts the marble back in the bag. Each of the first four times Erik takes out a marble, he gets a black marble.

A. What is the theoretical probability of Erik picking a black marble next time? Based on Erik's results, what is the experimental probability of Erik picking a black marble next time?

B. Explain the difference between the two probabilities you found in part A.

C. What is the theoretical probability and likelihood of getting four black marbles in a row?

Answer 1

A) there are three colors of marbles and an equal number of each marble. Therefore, the theoretical probability of getting a black marble is 1/3. As for the experimental probability, divide the number of times Erik got a black marble by the total number of marbles he picked.

B) this is a definition based question. By definition the theoretical probability is defined as the total number of favorable outcomes / total # of outcomes. In this case, the “favorable” outcome is black since we’re calculating the probability of getting a black marble. Experimental probability is the *actual* number of favorable outcomes obtained in an experiment divided by the total number of outcomes in an experiment.

C) to get the theoretical probability of getting four black marbles, take the theoretical probability of getting *one* marble and multiplying by itself four times.