What is the chance of getting $100\%$ in $50$ questions paper If I have a test with one question which is true or false, the chances of getting $100\%$ in the exam is $50\%$ as I can select a right or wrong answer.
But what is the chance (exact percentage figure) of getting $100\%$  in a test where there are $50$ questions, each having true or false?
Thanks
 A: Assuming that you’re guessing on each question, so that the probability of getting any given question right is $\frac12$, the probability of guessing right on all $50$ questions is $\left(\frac12\right)^{50}$. This is a little more than $8.88\times 10^{-16}$.
A: Note that the probability of randomly choosing and answer/guessing and getting any ONE answer correct is $50\% = 1/2$. 
But to get all $50$ answers correct, if guessing on each, the probability of getting $100\%$ is 
$$\underbrace{\dfrac 12 \times \dfrac 12 \times \cdots \times \dfrac 12}_{\large 50\;\;\text{times}} \quad = \quad \left(\frac 12\right)^{50}$$
A: The probablility would be 1/2 for each question, you would multiply (1/2) by itself 50 times. That would equal 8.882*10^-16, a very small number. However, this would not be a real-life situation, because most of the time you would have at least some knowlege of the quesitons.Also, you would use guessing to eliminate incorrect choices, and that might increase your chances of getting a correct answer above the number mentioned. 
