Question

Nina wanted to test if her 6-sided die was fair. In other words, she wanted

to test if some sides get rolled more often than others. She rolled the die
60 times and recorded how often each side was rolled. Here are her
results:
Side
1 2 3
4 5 6
Observed counts 10 7 9 11 9 14
Nina wants to perform a x² goodness-of-fit test to determine if these
results give convincing evidence that her die is unfair.
What is the expected count of rolls to land showing a 3?
You may round your answer to the nearest hundredth.
Expected:
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Answer 1

To calculate the expected count of rolls to land showing a 3, we need to first calculate the expected probability of rolling a 3, assuming the die is fair. Since there are six sides to the die, each side has an equal probability of 1/6 of being rolled.

Therefore, the expected probability of rolling a 3 is 1/6.

To calculate the expected count, we multiply the expected probability by the total number of rolls:

Expected count = (1/6) * 60
Expected count = 10

Therefore, the expected count of rolls to land showing a 3 is 10.

Answer 2

The expected count of rolls to land showing a 3 is 10.00.