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.

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:

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)=

In a lucky dip game ten wrapped items are stored in a bin. One item is a rotten egg and has been included as a prank. Jennifer draws an item from the bin. What is her probability of obtaining the rotten egg (round your answer to one decimal place)?

Becca plays a game in which she can purchase a ticket. Each ticket has several chances, or "catches," to win money.The table below shows the probability of winning at each stage, and how much money the ticket can win at each catch. Every time Becca plays the game, her ticket is played through each catch, which means she can win money at each stage.Catch Probability WinningsCatch 0 40% $1Catch 1 45% $5Catch 2 12% $10Catch 3 3% $25Given the probabilities and payout values in this table, what is the expected value of Becca's ticket?a.)$4.60b.)$1.20c.)$10.25d.)$41.00

A dartboard has 5 equally sized slices numbered from 1 to 5.Some are grey and some are white.The slices numbered 3 and 4 are grey.The slices numbered 1, 2, and 5 are white.A dart is tossed and lands on a slice at random.Let X be the event that the dart lands on a grey slice, and let PX be the probability of X.Let not X be the event that the dart lands on a slice that is not grey, and let Pnot X be the probability of not X. (a)For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Event Outcomes Probability1 2 3 4 5X =PXnot X =PnotX(b)Subtract.=−1PX (c)Select the answer that makes the sentence true.−1PX is the same as ▼(Choose one).