Part 2: Carnival Games At the carnival, you may remember a game where you throw darts to pop two balloons from a wall. The balloons may have prize tokens. For the next player... . There are 50 balloons on the wall and 21 of them each contain a prize token. • The next player pays $2 and gets to throw darts until they pop 2 balloons. Their winnings are based on how many prize tokens they collect. See the table below. Note: The payout of tokens does NOT take into consideration the $2 the player paid. Find the expected value for this game for the next player. Find who the game favors. Complete the tree diagram using non-simplified fractions to label the probabilities. Use T for token and NT for no token. On the right of the tree, list the four outcomes and their final probabilities using non-simplified fractions. Check these add to one. START 1 balloon with a token (T) Use the outcomes' probabilities from the tree to find the expected value of this game. Use all four probabilities in the expected value chart to account for all possibilities. Number of tokens Probability Payout Value = (payout $2 cost) Expected Value for each row 0 $0 2 balloon without a token (NT) $2 $5 Total Expected Value for the player → Does the game favor the player or the game runner?

A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do it? a.24           b. 12         c. 6        d. 42

A game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.

Please show all work for this problem