478. A basketball player scores an average of 18.6 points per game for five  games. How many points must he score in the next game to raise his average to 20 points per game?

479. What is the average of 7 numbers if the average of the first two is 9 and the average of the last 5 is 16?

480. 42 is the arithmetic mean of a group of 30 numbers. If two numbers, 82 and 84, are removed, then what is the arithmetic mean of the remaining group of numbers?

481. 2 numbers x and y have a geometric mean of 12 and an arithmetic mean of 12.5. Find x² + y².

482. Joan’s average through five math tests was m, after a sixth test her average was n. If the teacher then decides to double the weigh of the last test, what will Joan’s average be?

483. The ace of hearts, the ace of clubs, the ace of diamonds and the ace of spades are face down on a table. Two different cards are selected at random from the set of four cards. What is the probability that at least one of the cards is a red ace?

484. In a raffle 20 tickets are sold. Two prizes will be given. A student buys 2 tickets. What is the arability that this student wins at least one prize?

485. A blue urn contains 4 black marbles and two blue marbles. A black run contains 4 black marbles and 11 blue marbles. One marble is drawn at random from each of the two urns. What is the probability that both of the marbles drawn are blue?

486. A teacher with a math class of 20 students randomly pairs the students to take a test. What is the probability that Camilla and Cameron, two students in the class, are paired with each other?

487. If there are 3 boys and 4 girls in a group and two are chosen to give a report, what is the probability that one boy and one girl are chosen?

488. The odds are 7 to 15 against horse Car Naggy winning the third race at Upson Downs. What is the probability that a different horse will win?

489. The probability of rain on any given day in Atlanta is 20%. After how many days would you expect it to have rained on 30 days?

490. The probability that a baseball player gets a hit is 3/10. Find the probability that she gets 2 hits in 4 at bats in her next game.

491. Two digits between 1 and 9, inclusive, are selected at random. The same digit may be selected twice. What is the probability that their product is a multiple of 3?

492. If five standard fair dice are tossed simultaneously, what  is the probability that the outcome has a sum greater than 28?

493. Eight first-graders, 4 girls and 4 boys, arrange themselves at random around a merry-go-round. What is the probability that boys and girls will be seated alternately?

494. A secretary writes letters to 8 different people and addresses 8 envelopes with the peoples’ addresses. He randomly puts the letters in the envelopes. What is the probability that he get exactly 6 letter in the correct envelopes?

495. The integers from 1 to 10 , inclusive, are partitioned at random into two sets of five elements each. What is the probability that 1 and 2 are in the same set?

496. Ashley, Bob, Carol, and Doug are rescued from a desert island by a pirate who forces them to play a game. Each of the four, in alphabetical order by first names, is forced to roll two dice. If the total on the two dice is either 8 or 9, the person rolling the dice is forced to walk the plank. The game stops as soon as one player loses or after all has rolled the dice once. What is the probability that Doug survives?

497. Instead of using two standard cubical dice in a board game, three standard cubical dice are used so that the game goes more quickly. In the regular game, doubles are needed to get out of the ‘pit’. In the revised game, doubles or triples will get you out. How many times as likely is it for a player to get out of the ‘pit’ on one toss under the new rules as compared to the old rules?

498. Rocky and Bullwinklle are playing Risk. Rocky rolls one six sided die, while Bullwinkle rolls two of them. What is the probability that Rock’s roll is greater than or equal to Bullwinkle’s larger number?

499. Richard is hitchhiking from Decatur, AL, to Amherst, VA. The probability that Richard will see a car within the next 20 minutes is 609/625. What is the probability that he will see a car within the next 5 minutes? Assume that the probability of seeing a car at any moment is uniform (the same) for the entire 20 minutes.