Find the probability: At Hogwarts School of Witchcraft and Wizardry, the Sorting Hat chooses one of four houses for each first-year student. If 4 students are randomly selected from 10 available students, what is the probability that they are the four youngest students?

A middle school chess clob has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that Adam and Ella will be selected? A B D E 20 42 4 1

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?

If a card is picked at random from a standard 52-card deck, what is the probability of getting a spade or a face card? Note: there are 3 face cards in each suit (the King, Queen, and Jack).

There are 11 players on a baseball team, all with roughly equal athletic ability. The coach has decided to choose the players who will play the four infield positions (first base, second base, third base, and shortstop) randomly. Tori and Brittany are on a team. Determine the probability of Tori and Brittany being chosen to play in the infield

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).

There are eight different sizes of puzzles. Each person takes a turn selecting and keeps it. What is the probability that the first puzzle chosen is a 100-piece and the second is a 1000-piece puzzle?