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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

Answer:

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

Explanation:

Probability of guessing the first question correctly: #1/5#

For that #1/5# of the time when the first question has been guessed correctly, the second question could be guessed correctly #1/5# of the time. So the first two questions could be guessed correctly #1/5xx1/5=(1/5)^2# of the time.

Similarly the first three questions could be guessed correctly #(1/5)^3# of the time;

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

and all fives, #(1/5)^5# of the time.

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

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