Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of $12$ draws, Romain didn't get picked even once.
Let's test the hypothesis that **each brother has an equal chance of $\dfrac{1}{3}$ of getting picked in each draw** versus the alternative that Romain's probability is *lower*.
**Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of $12$ times? Round your answer, if necessary, to the nearest tenth of a percent.**
$\quad$[[☃ input-number 1]]
Let's agree that if the observed outcome has a probability *less* than $1\%$ under the tested hypothesis, we will reject the hypothesis.
**What should we conclude regarding the hypothesis?**
[[☃ radio 1]]