Question

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

Answer 1

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%`