First, we need to find the expected probability for each outcome. Since there are 6 equally likely outcomes on the cube, each outcome has a probability of 1/6. Therefore, the expected frequencies are:
Outcome: 2 4 6 8 10 12
Expected frequency: 15 15 15 15 15 15
To find the discrepancy between the experimental and expected probabilities, we can use the formula:
|Observed frequency - Expected frequency| / Expected frequency
We can calculate this for each outcome and take the maximum value as the discrepancy:
Outcome: 2 4 6 8 10 12
Frequency: 10 9 6 15 13 8
Expected frequency: 15 15 15 15 15 15
Discrepancy: 0.333 0.400 0.600 0 0.133 0.467
The smallest discrepancy is 0, which occurs for outcome 8. Therefore, the answer is 0 (rounded to the nearest thousandth).
Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the table. What is the smallest discrepancy between the experimental and the expected probability of this experiment? Write your answer in 3 decimal places, rounded to the nearest thousandth.
1 answer
5 answers