Homework Week 12

Problem 1

What is the probability that a card selected at random from a standard deck of 52 cards is an ace?

Problem 5

What is the probability that the sum of the numbers on two dice is even when they are rolled?

Problem 9

What is the probability that a five-card poker hand does not contain the queen of hearts?

Problem 13

What is the probability that a five-card poker hand contains at least one ace?

Problem 15

What is the probability that a five-card poker hand contains two pairs, that is, two of each of two different kinds and a fifth card of a third kind?

Problem 17

What is the probability that a five-card poker hand contains a straight, that is, five cards that have consecutive kinds? Note: An ace can be considered either the lowest card of an A-2-3-4-5 straight or the highest card of a 10-J-Q-K-A straight.

Problem 23

What is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7?

Problem 25

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding:

1. 50
   
2. 52
   
3. 56
   
4. 60

Problem 27

Find the probability of selecting exactly one of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding:

1. 40
   
2. 48
   
3. 56
   
4. 64

Problem 33

What is the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, in a drawing if 200 people enter a contest and:

1. no one can win more than one prize.
   
2. winning more than one prize is allowed.

Problem 37

Which is more likely: rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled?

Problem 40

A player in the Powerball lottery picks five different integers between 1 and 69, inclusive, and a sixth integer between 1 and 26, which may duplicate one of the earlier five integers. The player wins the jackpot if all six numbers match the numbers drawn.

1. What is the probability that a player wins the jackpot?
   
2. What is the probability that a player wins $1,000,000, which is the prize for matching the first five numbers, but not the sixth number, drawn?
   
3. What is the probability that a player wins $100 by matching exactly three of the first five and the sixth numbers drawn, or four of the first five numbers, but not the sixth number, drawn?
   
4. What is the probability that a player wins a prize of $4, which is the prize when the player matches the sixth number, and either one or none of the first five numbers drawn?