HENRY PROGRAMMED A CALCULATOR TO RANDOMLY DISPLAY A DIGIT FROM 0 THROUGH 9. THE RESULTS OF THE FIRST 50 DISPLAYS ARE SHOWN ON THE TABLE BELOW. WHAT IS THE POSITIVE DIFFERENCE BETWEEN THE THEORETICAL PROBABILITY AND EXPERIMENTAL PROBABILITY FOR GETTING A 9 IF EACH DIGIT HAS AN EQUAL CHANCE OF BEING DISPLAYED? EXPRESS ANSWER AS PERCENT.
DIGIT FREQUENCY
0 llllll
1 1111
2 111111
3 1111
4 111111
5 11111
6 111111
7 111
8 111
9 1111111
total 50
* 1 stands as tally mark
oops 0 is 0 111111
its 6 tally marks
theory: 1/10 = .10
actual: 7/50 = .14
difference = .04 = 40% of .10
To find the theoretical probability of getting a 9 if each digit has an equal chance of being displayed, we need to determine the ratio of the number of favorable outcomes (getting a 9) to the total number of possible outcomes (total displays), assuming all digits are equally likely.
The theoretical probability of getting a 9 can be calculated as follows:
The number of favorable outcomes (getting a 9) = 1111111 (from the table)
The total number of possible outcomes (total displays) = 50 (from the table)
The theoretical probability of getting a 9 = (Number of favorable outcomes) / (Total number of possible outcomes)
= 1111111 / 50
= 22222.22 (rounded to 2 decimal places)
Now, let's calculate the experimental probability of getting a 9 based on the given data:
The frequency of getting a 9 = 1111111 (from the table)
The experimental probability of getting a 9 = (Frequency of getting a 9) / (Total number of displays)
= 1111111 / 50
= 22222.22 (rounded to 2 decimal places)
To find the positive difference between the theoretical probability and experimental probability, we can subtract the experimental probability from the theoretical probability.
Positive difference = Theoretical probability - Experimental probability
= 22222.22 - 22222.22
= 0
Therefore, the positive difference between the theoretical probability and experimental probability for getting a 9 is 0%.