We are given a bag that contains 5 marbles with different colors. A marble is drawn and its color is recorded. Then the marble is placed back in the bag. The marbles have been drawn 30 times. The table shows the results of 30 drawings.
Drawing Results
White
Black
Red
Green
Blue
5
6
8
2
9
Now we will identify the marble that has an experimental probability of drawing it that is the same as the theoretical probability. Let's recall how the experimental and the theoretical probabilities are calculated.
Theoretical Probability
Number of favorable outcomes/Total number of outcomes
Experimental Probability
Number of successes/Number of trials
There are 5 possible outcomes when drawing a marble: white, black, red, green, and blue. Also, all outcomes are equally likely, so the theoretical probability of drawing any marble equals 1 5. Now we will find the experimental probabilities by using the outcomes in the given table. Note that to compare the probabilities we will expand the theoretical probabilities by 6.
Theoretical Probability
Experimental Probability
Comparison of the Probabilities
Drawing White
1/5=6/30
5/30
1/5≠5/30 *
Drawing Black
1/5=6/30
6/30
1/5=6/30 âś“
Drawing Red
1/5=6/30
8/30
1/5≠8/30 *
Drawing Green
1/5=6/30
2/30
1/5≠2/30 *
Drawing Blue
1/5=6/30
9/30
1/5≠9/30 *
As we compare the probabilities of drawing a marble, for the black marble the experimental probability of drawing it is the same as the theoretical probability.
