The winners of a carnival game draw a ticket from a box to determine their prize. Each winner draws a ticket and places it back into the box before the next draw. Every winner has a 28% chance of getting a pencil pouch, a 56% chance of getting a backpack, and a 16% chance of getting a gumball.The game operator wants to simulate what could happen for the next ten winners.So for each winner, she generates a random whole number from 1 to 100.She lets 1 to 28 represent a winner getting a pencil pouch, 29 to 84 a backpack, and 85 to 100 a gumball.Here is the game operator's simulation.Winner 1 2 3 4 5 6 7 8 9 10Random number 46 71 66 72 32 55 7 59 4 28In the simulation, which prize did each winner get?(a) Winner 4: (b) Winner 9: (c) Winner 10:

Josh's Bakery is giving a treat to each customer at a grand opening event. Each customer spins a wheel to determine which treat they get. Every customer has a 23% chance of getting a cupcake, a 23% chance of getting a brownie, and a 54% chance of getting a muffin.Josh wants to simulate what could happen for the first ten customers.So for each customer, he generates a random whole number from 1 to 100.He lets 1 to 23 represent a customer getting a cupcake, 24 to 46 a brownie, and 47 to 100 a muffin.Here is Josh's simulation.Customer 1 2 3 4 5 6 7 8 9 10Random number 39 96 4 40 22 88 75 28 8 52In the simulation, which treat did each customer get?(a) Customer 2: (b) Customer 4: (c) Customer 9:

An organization in Texas organizes lucky draw this month. 1 thousand tickets are sold for 4$ each. Each has an equal chance of winning. 2 tickets will win 267$, 8 tickets will win 163$ and 13 tickets will win 40$. Let, the random variable 𝑋X denote the net gain from purchase of one ticket. What is the probability that 𝑋X takes the value less than 163? (Enter the answer correct to 4 decimal place)

John has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.This game is this: John chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an odd numbered card is drawn. He loses $3.40 if an even numbered card is drawn.(If necessary, consult a list of formulas.)(a) Find the expected value of playing the game.dollars(b) What can John expect in the long run, after playing the game many times?(He replaces the card in the deck each time.)John can expect to gain money.Hecanexpecttowindollarsperdraw.John can expect to lose money.Hecanexpecttolosedollarsperdraw.John can expect to break even (neither gain nor lose money).

Ann is playing a carnival game. She is blindfolded while she throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small, "M" for medium, "L" for large, or "XL" for extra-large. The board has 3 small balloons, 5 medium balloons, 2 large balloons, and 2 extra-large balloons. She hits one of the balloons at random and wins a stuffed animal of that size.SXLLSMMSMMMLXL(a) Find the odds in favor of Ann winning a medium stuffed animal.(b) Find the odds against Ann winning a medium stuffed animal.

There are three different types of circus prizes marked big (B)(𝐵) , medium (M)(𝑀) and little (L)(𝐿) . Each contains a certain number of red (R)(𝑅) and gold (G)(𝐺) balls, distributed as followsbig prize (B)(𝐵) : 7R7𝑅   and 6G6𝐺  medium prize (M)(𝑀) : 6R6𝑅   and 3G3𝐺  little prize (L)(𝐿) : 3R3𝑅   and 1G1𝐺      Your friend wins 3 big prizes, 1 medium prize and 2 little prizes. Without looking, you randomly reach into one of her prizes, and randomly take out one of its balls, which happens to be gold (G)(𝐺) . Calculate the probability that you were choosing from a big prize bag.P(B|G)=𝑃(𝐵|𝐺)=