Question

1) If you have a school report which has 53 rows of assessment criteria.
2) You have 5 marking criteria for each row (in terms of qualitative assessment)
3) What are the chances that a 2008 and a 2009 year report on the same child are exactly the same?
Thanks

Answer 1

Answer on Question #44508 – Math - Statistics and Probability

Problem.

1) If you have a school report which has 53 rows of assessment criteria.

2) You have 5 marking criteria for each row (in terms of qualitative assessment)

3) What are the chances that a 2008 and a 2009 year report on the same child are exactly the same?

Thanks

Solution.

There are $5^{53}$ ways to fill report (5 different possibilities for each row). Hence there are $5^{53} \cdot 5^{53}$ ways to fill 2008 and 2009 years reports. There are $5^{53}$ cases, when two reports are exactly the same. Therefore the probability equals

$$p = \frac{5^{53}}{5^{53} \cdot 5^{53}} = \frac{1}{5^{53}}.$$

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