We roll a six-sided die 60 times. The table shows the results.
Six-sided Die Results
Rolling 1
Rolling 2
Rolling 3
Rolling 4
Rolling 5
Rolling 6
11
14
7
10
6
12
Results show the number of trials in which a favorable outcome occurs —successes. Now we will identify the number that has a experimental probability of rolling it the same as its 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 6 possible outcomes when rolling a die: 1, 2, 3, 4, 5, and 6. Also, all outcomes are equally likely, so the theoretical probability of rolling any number equals 1 6. Now we will find the experimental probabilities by using the outcomes in the result table. In addition, to compare the probabilities we will expand the theoretical probabilities by 10.
Theoretical Probability
Experimental Probability
Comparison of the Probabilities
Rolling 1
1/6=10/60
11/60
1/6≠11/60 *
Rolling 2
1/6=10/60
14/60
1/6≠14/60 *
Rolling 3
1/6=10/60
7/60
1/6≠7/60 *
Rolling 4
1/6=10/60
10/60
1/6=10/60 âś“
Rolling 5
1/6=6/60
6/60
1/6≠5/60 *
Rolling 6
1/6=12/60
12/60
1/6≠5/60 *
As we compare the probabilities of rolling a dice, we can see that rolling 4 has an equal experimental probability and theoretical probability.
