Why is the probability for the signal at 160 in the bromine mass spectrum twice as high as for the signals at 158 and 162?
All possible arrangements of $\ce{Br2}$ molecule:


$\displaystyle 79 + 79 = 158$
$\displaystyle \color{red}{79 + 81} = 160$
$\displaystyle \color{red}{81 + 79} = 160$
$\displaystyle 81 + 81 = 162$


The amount of $\ce{^{79}Br}$ and $\ce{^{81}Br}$ in nature is roughly the same, thus each permutation is equally probable. There are two arrangements that lead to $160$. While $158$ and $162$ each have only one arrangement. Therefore $160$ is twice as likely to be found compared to other masses.