Lesson 5.2.1

HW: 5-29 to 5-33

Learning Target: Scholars will review and then continue developing their understanding of uniform probability models, including the complement of an event.

Have you ever played a game where everyone should have an equal chance of winning, but one person seems to have all the luck? Did it make you wonder if the game was fair? Sometimes random events just happen to work out in one player’s favor, such as flipping a coin that happens to come up heads four times in a row. But it is also possible that games can be set up to give an advantage to one player over another. If there is an equal chance for each player to win a game, then it is considered to be a fair game. If it is not equally likely for each player to win, a game is considered to be unfair.

 In this lesson you will continue to investigate probability. As you work, ask these questions in your study team:

 How many outcomes are possible?

 How many outcomes are desirable?

5-23. PICK A CARD, ANY CARD

What is the probability of picking the following cards from the deck? Write your response as a fraction, as a decimal, and as a percent.Explore probability with cards using5-23 Student eTool(CPM).

  1. P(black)?
  2. P(club)?
  3. If you drew a card from the deck and then replaced it, and if you repeated this 100 times, about how many times would you expect to draw a face card (king, queen, or jack)? Explain your reasoning.

5-24.Sometimes it is easier to figure out the probability that something will not happen than the probability that it will happen. When finding the probability that something will not happen, you are finding the probability of the complement. Everything in the sample space that is not in the event is in the complement.

  1. What is the probability you do not get a club, written P(not club)?
  2. What is P(not face card)?
  3. What would happen to the probability of getting an ace on a second draw if you draw an ace on the first draw and do not return it to the deck? Justify your answer.

5-25. Rob decided to play a card game with his friend, Travis. He told Travis that if he picked a black card with a value of nine or greater, Travis would win. (Jacks, queens, and kings are considered to be greater than nine.) If Rob picked a red card with a value of less than nine, Rob would win. (Aces are considered to have the value of one in this case.)

  1. What is the probability that Travis will win?
  2. What is the probability that Rob will win?
  3. According to the definition in the introduction to this lesson, is this a fair game? Why or why not?

5-26. The city has created a new contest to raise funds for a big Fourth of July fireworks celebration. People buy tickets and scratch off a special section on the ticket to reveal whether they have won a prize. One out of every five people who play get a free entry in a raffle. Two out of every fifteen people who play win a small cash prize.

  1. If you buy a scratch-off ticket, is it more likely that you will win a free raffle ticket or a cash prize? Explain your answer.
  2. What is the probability that you will win something (either a free raffle entry or a cash prize)?
  3. What is the probability that you will win nothing at all? To justify your thinking, write an expression to find the complement of winning something.

5-29.Find the probability of each event. Write your answer as a fraction and as a percent.

  1. Drawing a diamond from a standard deck of cards.
  2. Rolling a number less than five on a standard number cube.
  3. Drawing a blue marble from a bag of 18 marbles, three of which are blue.

5-30.Imagine a standard deck of cards with all of the aces and twos removed. Find each probability below.Explore cards with theProbability eTool.

  1. P(heart)
  2. P(black)
  3. P(face card)
  4. How is the P(face card) different with this deck from the probability if the deck was not missing any cards? Which probability is greater? Why?
  5. P(not heart)

5-31. The Kennedy High School cross-country running team ran the following distances in recent practices. 5-31 HW eTool (CPM).

  • 3.5 miles, 2.5 miles, 4 miles, 3.25 miles, 3 miles, 4 miles, and 6 miles.
  • Find the mean and median of the team’s distances.

5-32. Find the area of each figure below.

5-33. Simplify the following expressions using the order of operations.

  1. 3(8 − 4) + 42 − (2 + 3)
  2. 7 · 4 − 3 · 8 + 22 − 6
  3. 7 − (−3) + (−4 + 3)
  4. −6 −4(3 · 2) + 5

Lesson 5.2.1

  • 5-23.See below:
  • , 50%, or 0.5
  • , 25%, or 0.25
  • There areface cards, and 100 is just less than twice 52; so, since 2· 12 = 24, about 22 or 23 times.
  • 5-24.See below:
  • , 75% or 0.75
  • , about 77% or 0.769
  • There would be 3 aces left out of 51 cards so the probability would change.
  • 5-25. See below:
  • ≈ 0.19≈ 19%
  • ≈ 0.31≈ 31%
  • No, Rob has a better chance of winning.
  • 5-26.See below:
  • More likely to win a raffle ticket, because.
  • P(win something) - P(raffle ticket) + P(cash),
  • P(not win) = 1− P(win) = 1−
  • 5-29.See below:
  • or 25%
  • or≈ 66.67%
  • or≈ 16.67%
  • 5-30. See below:
  • P(face card) with a normal deck is. It is more likely to draw a heart in the modified deck because there are fewer non-face cards.
  • 5-31.mean =3.75 miles, median =3.5 miles
  • 5-32.See below:
  • 459 sq. in
  • 93.38 sq m
  • 5-33. See below:
  • 23
  • 2
  • 9
  • −5