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To calculate the expected probability for each outcome, we divide the frequency of each outcome by the total number of trials:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability for 2: 10/61 ≈ 0.164
Expected probability for 4: 9/61 ≈ 0.148
Expected probability for 6: 6/61 ≈ 0.098
Expected probability for 8: 15/61 ≈ 0.246
Expected probability for 10: 13/61 ≈ 0.213
Expected probability for 12: 8/61 ≈ 0.131
Now, we subtract the expected probability from the experimental probability for each outcome and find the smallest discrepancy:
|2 - 0.164| = 0.000
|0.222 - 0.148| = 0.074
|0.111 - 0.098| = 0.013
|0.165 - 0.246| = 0.081
|0.213 - 0.213| = 0
|0.142 - 0.131| = 0.011
The smallest discrepancy is 0.011.