A die is weighted so that the number $6$ comes up three times as often as any other number and all other numbers have the same probability of occurring. What is the probability of rolling a $1$ or a $6$?
A. $\dfrac 23$ $\quad$ B. $\dfrac 12$ $\quad$ C. $\dfrac 38$ $\quad$ D. $\dfrac 13$ $\quad$ E. $\dfrac 14$
Please explain how you got the answer!
If $6$ is three times as likely to be rolled, and the others all have equal probability, then the probability of rolling a $6$ would be $\frac 38$, and the other numbers all $\frac 18$. The probability of rolling a $1$ or a $6$ would be $$\frac 38+\frac 18=\frac 12$$