# Determine the probability of the given complementary event

12. Determine the probability of the given complementary event. What is the probability of randomly selecting a day of the week and not getting a day that begins with the letter t?

The probability is____.(Type an integer or a simplified fraction.)

13. Use the theoretical method to determine the probability of the given outcome or event.

A bag contains 20 red candies, 5 blue candies, and 10 yellow candies. What is the probability of drawing a red candy? A blue candy? A yellow candy? Something besides a yellow candy?

The probability of drawing a red candy is_______ (Round to the nearest hundredth as needed.)

The probability of drawing a blue candy is______ (Round to the nearest hundredth as needed.)

The probability of drawing a yellow candy is_____ (Round to the nearest hundredth as needed.)

The probability of drawing something besides a yellow candy is____(Do not round until the final answer. Then round to the nearest hundredth as needed.)

16. A multi-state lottery advertises the prizes and probabilities of winning shown in the accompanying table for a single $1ticket. The jackpot is variable, but assume it has an average of $3 million. Note that the same prize can be given to two outcomes with different probabilities. What is the expected value of a single lottery ticket? If you spend $365 per year on the lottery, how much can you expect to win or lose?

Use the icon to view the lottery prizes and probabilities table.

Prize Probability

Jackpot 1 in 73,093,170

$150,000 1in 2,412,253

$5,000 1 in 365,393

$150 1 in 9,753

$100 1 in 7,574

$5 1 in 255

$5 1 in 548

$2 1 in 91

$1 1 in 56

Part 1What is the expected value of a single lottery ticket?______ dollars (Round to the nearest cent as needed.)Part 2If you spend $365 per year on the lottery, how much can you expect to win? ______ dollars (Round to the nearest cent as needed.)17. In the game of roulette, when a player gives the casino $13 for a bet on the number 18, the player has a 37/38 probability of losing $13 and a 1/38 probability of making a net gain of $455. (The prize is $468, but the player’s$13 bet is not returned, so the net gain is $455.) If a player bets $13 that the outcome is an odd number, the probability of losing $13 is 20/38 and the probability of making a net gain of $13 is 18/38. (If a player bets $13 on an odd number and wins, the player is given $26 that includes the bet, so the net gain is $13.) Complete parts(a) through(c) below a. If a player bets $ 13 on the number 18, what is the player’s expected value? The expected value is_____ dollars. (Round to the nearest cent as needed.)b. If a player bets 3$that the outcome is an odd number, what is the player’s expected value? The expected value is negative _____ dollars.(Round to the nearest cent as needed.)

c. Is the best option to bet on 25, to bet on odd, or not to bet? Why? A. Betting on 25 is best because it has the highest potential net gain. B. Not betting is best because it has the highest expected value. C. Betting on odd is best because it has the highest expected value. D. Betting on odd and not betting are equally good because their expected values are higher than the expected value of betting on. 18. An MP3 player is loaded with 50 musical selections: 30rock selections, 8 jazz selections, and 12 blues selections. The player is set on “random play,” so selections are played randomly and can be repeated. Complete a through e.

a. What is the probability of the event that the first four selections are all jazz? The probability is______. (Round to four decimal places as needed.)

b. What is the probability of the event that the first five selections are all blues? The probability is_______. (Round to five decimal places as needed.)

c. What is the probability of the event that the first selection is jazz and the second is rock? The probability is _______. (Round to three decimal places as needed.)

d. What is the probability of the event that among the first four selections, none is rock? The probability is ______. (Round to four decimal places as needed.)

e. What is the probability of the event that the second selection is the same song as the first? The probability is ________. (Round to four decimal places as needed.)

19. The data in the following table show the outcomes of guilty and not-guilty pleas in 1,015 criminal court cases. What is the probability that a randomly selected defendant either pled guilty or was sent to prison?

Guilty plea Not-guilty plea

Sent to prison 378 52

Not sent to prison 566 19

The probability that a randomly selected defendant either pled guilty or was sent to prison is_____. (Round to the nearest thousandth as needed.)

20. The following table summarizes data on 984 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. Pedestrian intoxicated?

Yes No

Driver intoxicated? Yes 65 83

No 261 575

If one of the pedestrian deaths is randomly selected, the probability that the pedestrian was intoxicated or the driver was intoxicated is_______.(Round to the nearest thousandth as needed.)