What would the odds be to get 100% on a multiple choice exam where I guessed the answer to all 50 of the multiple choice questions (5 choices per questions)?

A 1 in how many chance?


closed as off-topic by George V. Williams, Mike Pierce, Paramanand Singh, user223391, Jonas Meyer Jul 4 '15 at 7:00

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – George V. Williams, Mike Pierce, Paramanand Singh, Community, Jonas Meyer
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    $\begingroup$ "experimental mathematics" lol $\endgroup$ – Alex Mathers Jul 3 '15 at 19:35

In every answer, you have $\frac15$ chance to guess the correct answer. You need that chance to occur all the $50$ time, and since all of your answers are independent events, you need to multiply these probabilties, therefore your chance: $(\frac{1}{5})^{50}=\frac{1}{5^{50}}$, which is not too big, you should learn for your exams. :)

  • 1
    $\begingroup$ I believe that you meant $(1/5)^{50}$, not $(1/50)^{50}$. $\endgroup$ – Mark Viola Jul 3 '15 at 19:50
  • $\begingroup$ Yes, thanks for correcting. $\endgroup$ – Atvin Jul 3 '15 at 20:49
  • 1
    $\begingroup$ You're welcome. My pleasure! And +1 for the answer $\endgroup$ – Mark Viola Jul 3 '15 at 21:06

Not the answer you're looking for? Browse other questions tagged or ask your own question.