To determine if the die is unbiased, we need to compare the expected probability of getting a 5 or 6 on a fair die to the actual proportion of 5 or 6 throws in the given data.
1. Expected probability of throwing a 5 or 6 on a fair die:
- Total number of possible outcomes on a die: 6 (1, 2, 3, 4, 5, 6)
- Probability of getting a 5 or 6 on one throw: 2/6 = 1/3
2. Actual proportion of 5 or 6 throws in the given data:
- Number of times a 5 or 6 was obtained: 3240
- Total number of throws: 9000
- Proportion of 5 or 6 throws: 3240/9000 = 0.36 or 36%
Since the expected probability of getting a 5 or 6 on a fair die is 1/3 (33.33%), and the actual proportion of 5 or 6 throws in the given data is 36%, it appears that the die may be biased towards 5 or 6. Further statistical analysis, such as hypothesis testing, may be needed to verify if the die is truly biased.
A die was thrown 9000 times and a throw of 5or 6 was obtained 3240 times. On the assumption of random throwing do the data indicate an unbiased die
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