1. An investment counselor calls witrh a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $30,000. If the economy grows at a moderate pace, the investment will result in a profit of $20,000. However, if the economy goes into recession, the investment will result in a loss of $30,000. You contact an economist who believes there is a 30% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace. and a 10% probability the economy will slip into recession. What is the expected profit from this investment?
The expected profit is
2. In the game of roulette, a player can place a $8 bet on the number 22 and have a 1/38 probability of winning. If the metal ball lands on 22, 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 takes 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?
The expected value is?
The player would expect to lose about?
3. According to a survey, 63% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded.
(a) Find the probability that exactly 38 of the murders were cleared.
(b) Find the probability that between 35 and 37 of the murders, inclusive, were cleared.
(c) Would it be unusual if fewer than 18 of the murders were cleared? Why or why not?
(a) Find the probability that exactly 38 of the murders were cleared is
(b) The probability that between 35 and 37 of the murders, inclusive, were cleared is
(c) Would it be unusual if fewer than 18 of the murders were cleared? Why or why not