a lottery game, 4 numbers are chosen at random. Each number can take a value 1, 2, 3, or 4, and each value is equally likely. The numbers are chosen independently of each other. Use the method of equally likely outcomes to answer the following question: Which sequence of numbers is more likely to be drawn in the lottery, 1-1-1-1 or 4-2-3-1?

Ravi is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized slices, as shown below. The wheel has 2 black slices, 4 grey slices, and 4 white slices. When the wheel is spun, the arrow stops on a slice at random. If the arrow stops on the border of two slices, the wheel is spun again. (a) If the arrow stops on a grey slice, then Ravi wins a gift card. Find the odds against Ravi winning a gift card. 0 (b) If the arrow stops on a grey slice, then Ravi wins a gift card. Find the odds in favor of Ravi winning a gift card. X to

Laura has a bag with 8 balls numbered 1 through 8. She is playing a game of chance. This game is this: Laura chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $14 if 7 or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Laura expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.) O Laura can expect to gain money. She can expect to win dollars per selection. O Laura can expect to lose money. She can expect to lose dollars per selection. O Laura can expect to break even (neither gain nor lose money). X

40 Jennie's teacher told her to select two problems from a list of two C-level problems, five B-level problems, and one A-level problem. If she selected at random, what is the probability that she se- lected two B-level problems?

Jina has a bag with 8 balls numbered 1 through 8. She is playing a game of chance. This game is this: Jina chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, S3 if the number 3 is selected, S4 if the number 4 is selected, and $5 if the number 5 is selected. She loses $5 if 6, 7, or 8 is selected. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. | dollars (b) What can Jina expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.) O Jina can expect to gain money. She can expect to win | dollars per selection. O Jina can expect to lose money. She can expect to lose dollars per selection. O Jina can expect to break even (neither gain nor lose money).

Two dice, a 8-sided one and a  10-sided one are shaken in a cup then "rolled" onto a table.  How many possible outcomes are there?