The War of \(1812\) started with a declaration of war on Thursday, June \(18\), \(1812\). The peace treaty to end the war was signed \(919\) days later, on December \(24\), \(1814\). On what day of the week was the treaty signed? $$\textbf{(A)}\ \text{Friday} \qquad \textbf{(B)}\ \text{Saturday} \qquad \textbf{(C)}\ \text{Sunday} \qquad \textbf{(D)}\ \text{Monday} \qquad \textbf{(E)}\ \text{Tuesday} $$
Tags: dates,calendar,days
Source: AMC 12 2016 B Q5
Elo Rating: 1500.00
A player chooses one of the numbers \( 1\) through \( 4\). After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered \( 1\) through \( 4\). If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins \( \\)1\(. If the number chosen appears on the bottom of both of the dice, then the player wins \) \\(2\). If the number chosen does not appear on the bottom of either of the dice, the player loses \( \\)1$. What is the expected return to the player, in dollars, for one roll of the dice? $$\textbf{(A)}\ -\frac{1}{8}\qquad \textbf{(B)}\ -\frac{1}{16}\qquad \textbf{(C)}\ 0\qquad \textbf{(D)}\ \frac{1}{16}\qquad \textbf{(E)}\ \frac{1}{8}$$
Tags: probability,expectation,dice
Source: AMC 10 2007 B Q22
Elo Rating: 1500.00