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# A multiple choice test has 5 questions each with 5 possible answers. What is the probability of guessing all the questions correctly?

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Alan P. Share
Jun 12, 2016

Probability of guessing all 5 correctly: 1/3125=0.032%

#### Explanation:

Probability of guessing the first question correctly: $\frac{1}{5}$

For that $\frac{1}{5}$ of the time when the first question has been guessed correctly, the second question could be guessed correctly $\frac{1}{5}$ of the time. So the first two questions could be guessed correctly $\frac{1}{5} \times \frac{1}{5} = {\left(\frac{1}{5}\right)}^{2}$ of the time.

Similarly the first three questions could be guessed correctly ${\left(\frac{1}{5}\right)}^{3}$ of the time;

and the first four, 1/5)^4 of the time;

and all fives, ${\left(\frac{1}{5}\right)}^{5}$ of the time.

(1/5)^5=1/3125=0.00032=0.032%

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