In the game of roulette, a player can place a $8 bet on the number 34 and have a 1/38 probability of winning. If the metal ball lands on 34, the player gets to keep the $8 paid to play the game and the player is awarded an additional $280. Otherwise, the player is awarded nothing and the casino take the player's $8. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? Note that the expected value is the amount, on average, one would expect to gain or lose each game.

Which function has the smallest y-intercept value

Ling listed all of the factors of a mystery number: 1,2,4,8,16,32 what is the mystery number?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?