Chapter 13 Study Guide

Vocabulary

Review chapter 13 vocabulary.

Die Roll Probabilities

A die is rolled.
- P(2): Probability of rolling a 2. The probability of rolling a 2 on a standard six-sided die is $1/6$ .
- P(2 or 5): Probability of rolling a 2 or a 5. The probability of rolling a 2 or a 5 is $2/6 = 1/3$ .
- P(not 6): Probability of not rolling a 6. The probability of not rolling a 6 is $5/6$ .

Marble Probabilities

A bag contains 4 red, 3 green, 6 blue, and 2 yellow marbles.
- P(green): Probability of drawing a green marble. The probability of drawing a green marble is $3/15 = 1/5$ .
- P(yellow or red): Probability of drawing a yellow or red marble. The probability of drawing a yellow or red marble is $6/15 = 2/5$ .
- P(not red): Probability of not drawing a red marble. The probability of not drawing a red marble is $11/15$ .

Experimental vs. Theoretical Probability

Die roll experiment results are shown in a table.
- Experimental probability of rolling a 4: Determined from the experiment's results (Data required).
- Theoretical probability of rolling a 4: The theoretical probability of rolling a 4 is $1/6$ .

Card Drawing Probability

A card is drawn from a standard deck of 52 cards.
Probability of drawing a ten, six, or King: There are 4 tens, 4 sixes, and 4 kings in a deck of 52 cards. The probability is $12/52 = 3/13$ .

Sample Space Representation

Represent the sample space using a table or tree diagram.
- Baseball team shirts and pants: blue or white shirts with blue or white pants.
- Dance club shows: Sleeping Beauty or The Nutcracker at Symphony Hall or The Center for the Arts.

Coin Toss Probability

Tossing a coin four times.
- Probability of getting four tails: The probability of getting tails on one toss is $1/2$ . The probability of getting four tails in a row is $(1/2)^4 = 1/16$ .

Possible Outcomes

Decorating a room with one choice from each category.
- Outdoor patio plans: 4 types of stone, 3 types of edgers, 5 dining sets, and 6 grills.
  - Total possible outcomes: $4 \times 3 \times 5 \times 6 = 360$ .

Independent vs. Dependent Events

Drawing a king from a deck of 52 cards, then tossing a coin and landing heads up.
- Events are independent since the outcome of drawing a card does not affect the outcome of tossing a coin.
- Probability: (Probability of drawing a King) x (Probability of tossing heads) = $(4/52) \times (1/2) = 1/26$ .
Drawing a red marble from a bag of 2 blue and 5 red marbles and not replacing it, then drawing a second red marble.
- Events are dependent because not replacing the first marble changes the composition of the bag for the second draw.
- Probability: (Probability of drawing a red marble first) x (Probability of drawing a red marble second, given the first was red) = $(5/7) \times (4/6) = 10/21$ .

Probability Without Replacement

Drawing a king from a standard deck of 52 cards without replacement, then drawing a second king.
- Probability: $(4/52) \times (3/51) = 1/221$ .

Probability with Replacement

Randomly selecting 3 cards from a standard deck of 52 cards with replacement.
- Probability that none of the cards drawn are hearts: The probability of not drawing a heart is $39/52 = 3/4$ . With replacement, the probability of 3 draws in a row is $(3/4)^3 = 27/64$ .

Conditional Probability

A black shoe is selected from a bin of 6 black shoes and 4 brown shoes and not replaced.
- Probability that a second shoe selected will be black: $(5/9)$

Spinner Probability

A spinner with 12 evenly sized sections numbered 1 to 12 is spun.
- Probability that the number spun is 12 given that the number is even: The probability of getting 12 given even = $(1/6)$

Mutually Exclusive Events

Selecting a cat or dog at an animal shelter that has 15 cats, 25 dogs, 9 rabbits, and 3 horses.
- Events are mutually exclusive because you cannot select a cat and a dog at the same time.
- Probability: $(15+25) / (15+25+9+3) = 40/52 = 10/13$ .
Probability of drawing a card from a standard deck and not getting a spade: $39/52 = 3/4$ .
Probability of drawing a card from a standard deck and choosing a king or an ace: $(4+4)/52 = 8/52 = 2/13$ .
Probability of drawing a card from a standard deck and choosing a face or a club: There are 12 face cards (Jacks, Queens, Kings) and 13 clubs. 3 of the clubs are face cards so the total number of cards that are either a face card or a club is 12 + 13 - 3 = 22. The probability is therefore $22/52 = 11/26$ .

Probability with Parks and Recreation Department Classes

The table shows the Parks and Recreation Department classes and the number of participants aged 7-9.
- Probability that a participant chosen at random is in Drama or is an 8-year-old (Data from table is needed).
- Probability that a participant chosen at random is in Art or is a 9-year-old (Data from table is needed).

Daily Selfie Probability

Joe likes to take pictures of himself. On an average day, he takes about 12 selfies until he finds one that he likes and keeps. For the next day, what is the probability that he will keep the selfie?
- Probability: $1/12$

Picnic Combinations

Choosing one of each: 3 sandwiches, 2 chips, 2 drinks, and 3 desserts.
- Total combinations: $3 \times 2 \times 2 \times 3 = 36$ .

Coin Flip Probability

Flipping a coin three times in a row.
- Probability of getting 3 tails: $(1/2)^3 = 1/8$ .

Softball Player Hit Probability

A softball player got a hit in 20 of her last 50 at bats.
- Probability of a hit in her next at bat: $20/50 = 2/5$ .

Passcode Possibilities

5-digit passcode where digits cannot be repeated.
- Number of possibilities: $10 \times 9 \times 8 \times 7 \times 6 = 30240$ .

Arrangement Possibilities

Arranging 8 different shirts in a closet.
- Number of ways: $8! = 40320$ .

Horse Race Possibilities

Ten horses running in a race; finishing first, second, and third.
- Number of ways: $10 \times 9 \times 8 = 720$ .

Playlist Arrangements

A playlist of 8 songs.
- Arranging the first 3 songs: $8 \times 7 \times 6 = 336$ .
- Choosing 3 favorite songs: $\binom{8}{3} = \frac{8!}{3!(8-3)!} = 56$ .

Side Dish Combinations

Picking 2 side dishes from a list of 8.
- Number of possibilities: $\binom{8}{2} = \frac{8!}{2!(8-2)!} = 28$ .

Basketball Team Lineup

12 players on a basketball team.
- Picking a starting lineup of 5 players: $\binom{12}{5} = \frac{12!}{5!(12-5)!} = 792$ .
- Arranging those 12 players into the 5 different positions: $12 \times 11 \times 10 \times 9 \times 8 = 95040$

Marble Drawing Probability

A bag contains 5 black, 7 blue, and 3 red marbles.
- Probability of grabbing a blue marble and then a red marble: $(7/15) \times (3/14) = 1/10$ .

Coin and Die Probability

Probability of flipping a coin heads and then rolling a 5 with a die:
$(1/2) \times (1/6) = 1/12$ .

Geometric Probability

Finding the probability that a point chosen at random lies in the shaded region. (Figures are required)

Combined Probability with Spinner and Cards

A spinner has four equal sections of different colors.
- Probability the spinner lands on red and then you are dealt a red jack from a standard deck of cards:
  $(1/4) \times (1/52) = 1/208$ .

Conditional Probability with Eye Color and Glasses

Seniors at a small high school were asked about their eye color and if they wear glasses. (Data is provided in a table).
- $P(Blue | NG)$ : Probability of blue eyes given no glasses. (Needs Data to calculate)
- $P(NG | Brown)$ : Probability of no glasses given brown eyes. (Needs Data to calculate)
- $P(Glasses or Green)$ : Probability of glasses or green eyes. (Needs Data to calculate)
- $P(Glasses and Blue)$ : Probability of glasses and blue eyes. (Needs Data to calculate)

Tree Diagram Probability

7th (46%) and 8th graders (54%) surveyed on homework time (more than 1 hour).
- 60% of 7th graders answered “Yes,” 70% of 8th graders answered