5. What is the difference between a priori and a poste riori probability

9. Which of the following are examples of independent

events?

a. Obtaining a 3 and a 4 in one roll of two fair dice

b. Obtaining a n a ce a nd a k ing i n t hat order b y

drawing twice without replacement f rom a de ck

of cards

c. Obtaining a n a ce and a k ing in that order b y

drawing twice with replacement from a de ck of

card

d. A cloudy sky followed by rain

e. A full moon and eating a hamburger

10. Which of the following are examples of mutually

exclusive events?

a. Obtaining a 4 and a 7 in one draw from a deck of

ordinary playing cards

b. Obtaining a 3 and a 4 in one roll of two fair dice

c. Being male and becoming pregnant

d. Obtaining a 1 and an even number in one roll of a

fair die

e. Getting married and remaining a bachelor

11. Which of the following are examples of exhaustive

events?

a. Flipping a coin and obtaining ahead or a t ail

(Edge not allowed)

b. Rolling a die and obtaining a 2

c. Taking an exam and either passing or failing

d. Going out on a date and having a good time

13. If you draw a single card once from a deck of ordinary playing cards, what is the probability that it

will be

a. The ace of diamonds?

b. A 10?

c. A queen or a heart?

d. A 3 or a black card?

14. If you roll two fair dice once, what is the probability

that you will obtain

a. A 2 on die 1 and a 5 on die 2?

b. A 2 and a 5 without regard to which die has the 2

or 5

c. At least one 2 or one 5?

d. A sum of 7?

15. If you are randomly sampling one at a time with

replacement from a bag that contains eight blues

marbles, seven red marbles, and ive green marbles,

what is the probability of obtaining?

a. A blue marble in one draw from the bag?

b. Three blue marbles in three draws from the bag?

c. A red, a green, and a blue marble in that order in

three draws from the bag?

d. At least two red marbles in three draws from the

bag?

16. Answer the same questions as in Problem 1 5,

except sampling is one at a time without replacement. Other

17. You are playing the one-armed bandit (slot machine)

described in Practice Problem 8.10, p. 212. There are

three wheels, and on each wheel, there is a picture of

a lemon, a plum, an apple, an orange, a p ear, cherries, and a banana ( seven different pictures). You

insert your silver dollar and pull down the lever.

What is the probability that?

a. Three oranges will appear?

b. Two or anges and a banana will appear, without

regard to order?

c. At least two oranges will appear?

19. You are planning to win big at the race track. In a

particular race, there are seven horses entered. If the

horses are all equally matched, what is the probability

of your correctly picking the winner and runner-up?

20. A gumball dispenser has 38 orange gumballs, 30 purple

ones, and 18 yellow ones. The dispenser operates such

that one quarter delivers 1 gumball.

a. Using three quarters, what is the probability of

obtaining 3 gumballs in the order orange, purple,

orange?

b. Using one quarter, what is the probability of obtain[1]ing 1 gumball that is either purple or yellow?

c. Using three quarters, what is the probability that of

the 3 gumballs obtained, exactly 1 will be purple

and 1 will be yellow?

21. If two cards are randomly drawn from a deck of ordinary playing cards, one at a time, with replacement,

what is the probability of obtaining at least one ace?

24. A distribution of scores is normally distributed with

a mean u= 85 and a standard deviation

[1] 4.6. If

one score is randomly sampled from the distribution,

what is the probability that it will be

a. Greater than 96?

b. Between 90 and 97?

c. Less than 88?

29. An instructor at the U.S. Navy's underwater demolition school believes he has developed a new technique

for staying under water longer. The school commandant gives him permission to try his technique with

a student who has been randomly selected from t he

current class. As part of their qualifying exam, all students are tested to see how long they can stay under

water without an air tank. Past records show that the

scores are normally distributed with a mean [1] [1] 130

seconds and a standard deviation

[1] 14 seconds. If

the new technique has no additional effect, what is the

probability that the randomly selected student w ill

stay under water for

a. More than 150 seconds?

b. Between 115 and 135 seconds?

c. Less than 90 seconds?

A deck of cards has 52 cards. These are split evenly into 4 suits (spades and clubs that are black, and hearts and diamonds that are red) and there are 13 cards in each suit. You select one card, record what suit it is and then replace it back in deck and shuffle the deck before selecting the next card. If you select 6 cards in this manner what is the probability that more than 4 will be Diamonds?

You have recorded 15 movies (5 comedies, 4 dramas, and 6 biographies). You pick the "surprise me" mode for playback where your machine chooses one show and then deletes is once it is finished. If you watch three shows on one weekend what is the probability you will get exactly two dramas?

You work for a small company that advertises they will deliver food to you house in under 45 minutes or it is free. You keep track of all your company's deliveries and know that the mean delivery time is 38.5 minutes (St Dev = 5.6).What is the probability that the next delivery will take more than 45 minutes and be free?