A bag contains 2 gold marbles, 6 silver marbles, and 27 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win \( \$ 4 \). If it is silver, you win \( \$ 2 \). If it is black, you lose \( \$ 1 \). What is your expected value if you play this game?

4. Em uma escola, 20 estudantes participaram do grupo de recepşão e acolhida dos alunos. A Diretora da escola convocou esses estudantes para uma reunião e iria sortear um pre- sente a um desses alunos. Daniela participou da reunião em que faltaram 4 dos estudantes convocados. Qual a probabilidade de ela ser sorteada e receber o presente oferecido pela Diretora? \( \begin{array}{llll}\text { A) } \frac{1}{20} & \text { B) } \frac{4}{20} & \text { C) } \frac{16}{20} & \text { D) } \frac{1}{16}\end{array} \)

7. มีเหรียญที่แตกต่างกัน 3 เหรียญ และลูกเต๋าที่แตกต่างกัน 2 ลูก ถ้าโยนเหรียญและลูกเต๋าที่แตกต่างกัน ทั้งหมด จำนวนวิธีในการขึ้นหน้าของเหรียญและลูกเต๋าที่แตกต่างกันได้ทั้งหมดกี่วิธี เมื่อเหรียญขึ้นหน้า เหมือนกัน และลูกเต๋าขึ้นหน้าเหมือนกัน \( \begin{array}{ll}\text { ก. } 6 & \text { ข. } 12 \\ \text { ค. } 18 & \text { ง. } 48\end{array} \)

8. En una quiniela de futbol, ¿cuántas apues- tas diferentes es posible hacer con 13 par- tidos si el resultado que se marca para cada uno de ellos es \( \mathrm{L}= \) gana el equipo local, \( \mathrm{E}= \) empate y \( \mathrm{V}= \) gana el equipo visitante?

This year, there are seven freshmen, eight sophomores, ten juniors, and seven seniors are eligible to be on a committee. In how many ways can a dance committee of 8 students be chosen? In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. In how many ways can a dance committee be chosen if it is to consist of 4 juniors and 4 senions. Determine the probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. Write your answer in decimal form, rounded to the nearest thousandth. Answer:

Next question The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs \( \$ 5 \). There is 1 winning ticket out of the 180 tickets sold. The winner gets a prize worth \( \$ 84 \). Round your answers to the nearest cent. What is the expected value (to you) of one raffle ticket? \( \$-4.53 \) Walculate the expected value (to you) if you purchase 12 raffle tickets. \( \$-54.36 \) What is the expected value (to the PTO) of one raffle ticket? \( \$ 4.53 \) \( \$ \) PTO sells all 180 raffle tickets, how much money can they expect to raise for the classroom supplies? Question Help: Video