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Chapter 14 Homework

Math 1680 Spring 2008

1)You roll a pair of fair 6-sided dice.

a)What are the possible ways to get a total of 5?

b)What is the probability of getting a total of 5?

c)What are the possible ways to get a total of 10?

d)What is the probability of getting a total of 10?

2)You roll a pair of fair 6-sided dice.

a)How many ways are there to get a total of 7?

b)How many ways are there to get a total of 11?

c)Is it possible to roll a 7 and an 11 simultaneously?

d)What is the probability of getting a 7 and an 11 on one roll?

e)What is the probability of getting a 7 or an 11 on one roll?

3)You roll a pair of fair 6-sided dice.

a)How many ways are there to get an even number as your total?

b)How many ways are there to get a multiple of 3 as your total?

c)Can you roll an even number and a multiple of 3 simultaneously?

d)What is the probability of getting an even number and a multiple of 3 on one roll?

e)What is the probability of getting an even number or a multiple of 3 on one roll?

4)Suppose you draw one card from a well-shuffled standard deck.

a)What is the probability that you draw a face card? (A face card is a Jack, Queen, or King from any suit)

b)What is the probability that you draw a diamond?

c)What is the probability that you draw both a face card and a diamond?

d)What is the probability that you draw either a face card or a diamond?

5)A pair of dice is rolled 40 times. What is the probability of getting at least one double-ace (snake eyes)?

6)We play a game where you roll a die and I roll another die. You win if your die is higher than mine, and you lose otherwise.

a)What is the probability that you win the game?

b)If I roll first and get a 5, what is your probability of winning now?

c)If I roll first and get a 2, what is your probability of winning now?

7)A math teacher with no fashion sense picks his outfits at random each day. Each outfit consists of a shirt, a pair of pants, and a pair of shoes. One day, he has 5 different shirts, 4 different pairs of pants, and 3 different pairs of shoes to pick from. Since he has no fashion sense, he is equally likely to pick any shirt, pants, or shoes.

a)How many possible outfits could he make?

b)What is that probability that a specific outfit is chosen?

c)He decides he likes a certain shirtand chooses it. How many outfits are now available to him?

d)What is the probability he will complete the outfit with a specific pair of pants and shoes?

8)You throw a pair of fair 6-sided dice. What is the probability that at least one of the dice shows a 4?

9)You deal two cards off the top of a well-shuffled standard deck. For each pair of events, state whether

i) The first is more likely,

ii) The second is more likely,

iii) They are equally likely.

a)Drawing two hearts vs. drawing two Jacks

b)Drawing a Jack and then a King vs. drawing a King and then a Jack

c)At least one of the cards is a 7 vs. neither of the cards is a 7.

d)Drawing two cards of the same suit vs. drawing two cards of the same rank

10)You roll a fair 6-sided die, and then flip a fair coin as many times as the value of the roll (for example, if you roll a 3, you flip the coin 3 times). You count the number of heads.

a)Are the number of heads and the value of the die roll independent? Why or why not?

b)If you roll a 4, what is the probability of getting all 4 heads?

c)Without knowing what you roll yet, what is the probability of getting all heads?