Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(no prize is awarded to an athlete)

Students will be chosen at random for school spirit awards. There are $6$ athletes and $8$ non-athletes who are eligible for $2$ possible prizes. What is each probability? Explain how Exercises $12$ and $13$ are similar to Exercises $14$ and $15.$

Students will be chosen at random for school spirit awards. There are $6$ athletes and $8$ non-athletes who are eligible for $2$ possible prizes. What is each probability? $P$(no prize is awarded to an athlete)

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(no prize is awarded to an athlete)

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(both prizes are awarded to non-athletes)

At a high school, 40% of the students play an instrument. Of those students, 20% are freshmen. Of the students who do not play an instrument, 30% are freshmen. What is the probability that a student selected at random is a freshman who plays an instrument?

In a class of 25 students, 8 students have heights less than 65 inches and 10 students have heights of 69 inches or more. Find the probabilities described. P(greater than or equal to 65 inches)

Find the number of combinations. In how many ways can 11 contestants for an award be narrowed down to 3 finalists?

Find the number of permutations. How many ways can 12 runners in a race finish first, second, and third?

Do the possible arrangements represent permutations or combinations? Jennifer will invite 3 of her 10 friends to a concert.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. A class president, secretary, and treasurer are chosen from 12 students running for office.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. At the end of a season, 10 soccer teams are ranked by the state.

Do the possible arrangements represent permutations or combinations? Jennifer must decide how she and her 3 friends will sit at the concert.

Two marbles are chosen at random, one at a time from a box that contains 7 marbles, 5 red and 2 green, a. Find the probability of drawing 2 red marbles when the first marble is replaced before the second marble is chosen. b. Determine whether the situation described is independent.