The table below shows the results of a classroom activity involving rolling a fair number cube twenty-five times.
Outcome Frequency
1 IIIIIII
2 II
3 III
4 II
5 IIII
6 IIIIII
What is the difference between the theoretical probability of rolling an even number and the experimental results recorded in the table?
It is 12%
To calculate the theoretical probability of rolling an even number, we need to determine the total number of possible outcomes (which is 25 in this case) and the number of favorable outcomes (which are the even numbers 2 and 4, occurring twice each, totaling 4).
So, the theoretical probability of rolling an even number is 4/25 or 0.16.
Now let's calculate the experimental probability based on the results recorded in the table. The table shows that there are a total of 25 outcomes. Looking at the frequencies, we can see that there were a total of 2+2 = 4 even numbers rolled in the experiment.
So, the experimental probability of rolling an even number is 4/25 or 0.16.
Therefore, the difference between the theoretical probability and the experimental results is 0. Theoretical probability and experimental probability are the same in this case.
To find the difference between the theoretical probability of rolling an even number and the experimental results recorded in the table, we need to first determine the theoretical probability and then compare it to the actual results.
Theoretical Probability:
A fair number cube has 6 equally likely outcomes (numbers 1 to 6). Out of these 6 outcomes, 3 are even numbers (2, 4, and 6). Therefore, the theoretical probability of rolling an even number is 3/6, which can be simplified to 1/2 or 0.5.
Experimental Results:
From the table, we can see that there were 6 occurrences of rolling an even number (outcome 2 occurred 2 times and outcome 4 occurred 4 times). The total number of trials was 25.
Difference:
To calculate the difference between the theoretical probability and the experimental results, we subtract the experimental probability (number of occurrences of rolling an even number divided by the total number of trials) from the theoretical probability.
Experimental probability = 6/25 ≈ 0.24
Difference = Theoretical probability - Experimental probability
Difference = 0.5 - 0.24
Difference ≈ 0.26
Therefore, the difference between the theoretical probability of rolling an even number and the experimental results recorded in the table is approximately 0.26.