In an experiment, a standard die is tossed 600 times - Junior Cycle Mathematics - Question 2 - 2014
Question 2
In an experiment, a standard die is tossed 600 times. The results are partially recorded in the table below.
Number on die | 1 | 2 | 3 | 4 | 5 | 6
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Worked Solution & Example Answer:In an experiment, a standard die is tossed 600 times - Junior Cycle Mathematics - Question 2 - 2014
Step 1
Calculate the number of times that a 5 appeared.
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Answer
Let x be the number of times that a 5 appeared. We know that the total number of die tosses is 600, so:
92+101+115+98+x+105=600
By simplifying the equation, we find:
x=600−(92+101+115+98+105)x=600−511x=89
Thus, the number of times that a 5 appeared is 89.
Step 2
After looking at the results, Anne claims that the die is unbiased (fair). Do you agree with her? Give a reason for your answer.
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Answer
Yes.
Reason: If we tossed a fair die 600 times, we would expect each number to occur approximately 100 times. Since the frequencies of the outcomes are all relatively close to 100, we can conclude that the die appears to be unbiased.
Step 3
If this die is tossed 300 times, how many times would you expect to get an even number, based on the data in the table?
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Answer
Reason: Based on the results from the table, we determined that the die is fair. Therefore, we would expect that in 300 tosses, an even number would occur half the total number of times, so 150 times.
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