Question

{MEDAL} Suppose you have 20 tiles with the numbers 1 through 20. The theoretical probability that a tile chosen at random is a 5 is 1/20. If you pick a tile randomly, 20 times, replacing the chosen tile each time, will you get a 5 once? Explain

Answer 1

@mathstudent55 @Qwertty123

Answer 2

@Loser66

Answer 3

it is likely you will but not guaranteed. You can find the probability of getting the "5" tile exactly once using the binomial theorem

\[P(k=1) = \left(\begin{matrix}20 \\ 1\end{matrix}\right) (\frac{1}{20})(\frac{19}{20})^{19} = 0.377\]
you can also get probability of not getting a "5" tile
\[P(k=0) = (\frac{19}{20})^{20} = .358\]
Therefore probability of getting a "5" tile at least once is:
\[P(k>0) = 1 - .358 = 0.642\]