At the New York State Fair in Syracuse, Larry encounters a carnival game where for one dollar he may buy a single coupon allowing him to play a guessing game. On each play, Larry has an even chance of winning or losing a coupon. When he runs out of coupons he loses the game. However, if he can collect three coupons, he wins a surprise.

(a) What is the probability Larry will win the surprise?

(b) What is the expected number of plays he needs to win or lose the game.

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

Julian wrote the following numeric pattern on the board3,10,17,24,31,38.what numbers of julian's pattern are compound numbers.

Two airplanes start at the same place and travel in opposite directions, one at 395 miles per hour and the other at 422 miles per hour. how many hours will it take for the planes to be 2451 miles apart?