timothy, andrew, and leah are running for student council offices of president and treasurer. they could be…

Explanation:

Step1: Calculate total number of ways

There are 3 people running for 2 positions. The number of ways to fill 2 positions from 3 people is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 3$ and $r=2$. So $P(3,2)=\frac{3!}{(3 - 2)!}=\frac{3!}{1!}=3\times2=6$ ways.

Step2: Calculate number of ways Timothy is elected

If Timothy is elected, we consider two cases: Timothy as president (and one of the other 2 as treasurer) or Timothy as treasurer (and one of the other 2 as president). So there are 2 ways for Timothy to be elected for either position.

Step3: Calculate probability

The probability $P$ that Timothy is elected is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{2}{6}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$