A six sided die is rolled 150 times. The number 1 comes up 60 times. What is the experimental probability of rolling a 1? What is the theoretical probability of rolling a 1?
Experimental probability of rolling a 1: 60/150 = 0.4 or 40%
Theoretical probability of rolling a 1: 1/6 = 0.1666... or 16.6...%
To find the experimental probability of rolling a 1, you divide the number of times the event occurred by the total number of trials.
Experimental probability of rolling a 1 = Number of times event occurred / Total number of trials
In this case, the number of times the number 1 comes up is 60, and the total number of trials is 150.
Experimental probability of rolling a 1 = 60 / 150
Simplifying the fraction gives:
Experimental probability of rolling a 1 = 2 / 5 or 0.4
To find the theoretical probability of rolling a 1, you divide the number of successful outcomes by the total number of possible outcomes.
Theoretical probability of rolling a 1 = Number of successful outcomes / Total number of possible outcomes
Since a standard six-sided die has 6 possible outcomes (numbers 1-6), and there is only one number 1 on the die, the number of successful outcomes is 1.
Theoretical probability of rolling a 1 = 1 / 6
Therefore, the theoretical probability of rolling a 1 is 1/6 or approximately 0.1667.