Geometry Test-Chapter 12 Flashcards

Questions and Answers

What is the sample space?

the set of all possible outcomes

What is an outcome?

a possible result/answer of a probability experiment

For a family with 5 children, what is the probability that they have exactly 1 boy and 4 girls? (write answer as a fraction)

5/32

What is the probability of an event?

the likelihood an event will happen (from 0% to 100%) Signup and view all the answers

In what forms can answers be written?

decimal form (round to 3 decimals), fraction form (simplified fraction), percent (to the nearest tenth) Signup and view all the answers

What is a standard deck of cards?

52 cards, 4 suits (13 of each suit), 12 face cards in total (3 per suit) Signup and view all the answers

What is the theoretical probability?

favorable outcomes/ total # of outcomes Signup and view all the answers

What is the theoretical probability of pulling a queen out of a standard deck of cards (answer in fraction form)?

1/13 Signup and view all the answers

What is the formula for the probability of the complement of an event?

A̅ = 1 - P(A) Signup and view all the answers

What is the probability of not pulling a queen from a standard deck of cards?

12/13 Signup and view all the answers

What is geometric probability?

favorable area/ total area Signup and view all the answers

What is experimental probability?

<h1>of successes/ # of trials</h1> Signup and view all the answers

What are independent events?

one event does not affect the other; P (A and B) = P(A) x P(B) Signup and view all the answers

What are dependent events?

one event affects the other; P (A and B) = P(A) x P(B|A) Signup and view all the answers

What is the probability of selecting 3 blue marbles from a bag containing 10 red and 5 blue marbles when (a) replaced and (b) not replaced? (write answers in percent form)

(a) 3.7%, (b) 2.2% Signup and view all the answers

In a clothing store, if 75% of customers buy pants and 20% buy pants and a belt, what is the probability that a customer who buys pants also buys a belt?

26.7% Signup and view all the answers

Find and interpret the marginal frequencies from a two-way table given 53 females and 68 males surveyed on handedness.

121 total people are surveyed. 12 people are left-handed. 109 people are right-handed. Signup and view all the answers

What is joint frequency?

each entry in the table (data) Signup and view all the answers

What is marginal frequency?

the sums of the rows and columns (total) Signup and view all the answers

What is joint relative frequency?

a frequency divided by the total (relative aka probability) Signup and view all the answers

What is marginal relative frequency?

the sums of the joint relative frequencies (sum of probabilities) Signup and view all the answers

What is conditional relative frequency?

joint relative frequency/ row total Signup and view all the answers

What is the formula for overlapping events?

P(A) + P(B) - P(A and B) = P (A or B) Signup and view all the answers

What is the formula for disjoint or mutually exclusive events?

P(A) + P(B) = P(A or B) Signup and view all the answers

For a randomly selected card from a standard deck, what is the probability of (a) selecting an ace OR an 8 and (b) selecting a 10 OR a diamond? (write answers in decimal form)

(a) .154, (b) .308 Signup and view all the answers

What is the formula related to probabilities and tree diagrams?

(P(A) x P(B|A)) + (P(A̅) x P(B|A̅)) = P (B) Signup and view all the answers

What is a permutation?

an arrangement of objects in which order matters Signup and view all the answers

What is a factorial?

n! = n(n-1)(n-2)...(1) Signup and view all the answers

In a race with ten students, how many different ways can the students finish first, second, and third? (no ties)

720 ways Signup and view all the answers

What is a combination?

an arrangement of objects in which order does not matter Signup and view all the answers

In a playlist of 16 songs, how many combinations of 3 songs are possible?

560 ways Signup and view all the answers

How many ways can you arrange the letters in the word 'MISSISSIPPI'? (no letter repeats)

34650 ways Signup and view all the answers

What is a probability distribution?

a function that gives the probability of each possible value of a random variable; the sum of all probabilities must add up to 1 Signup and view all the answers

What is a histogram?

a graphical representation of frequency distribution Signup and view all the answers

What is a binomial distribution?

one type of probability distribution; shows the probabilities of the outcomes of a binomial experiment Signup and view all the answers

What is the formula for a binomial experiment?

P (K successes) = ₙCₖ (P)ᵏ (1-P)ⁿ⁻ᵏ Signup and view all the answers

According to a survey, about 62% of adults have visited a dentist in the past year. If you ask 5 randomly selected adults whether they have had a dentist visit in the past year, what is the most likely outcome of the survey?

The most likely outcome of the survey is that 3 out of 5 adults have visited a dentist in the past year. Signup and view all the answers

Study Notes

Probability Concepts

Sample Space: The complete set of all possible outcomes in a probability scenario.
Outcome: A specific result from a probability experiment.
Probability of an Event: Represents the chances of an event occurring, quantified as a percentage (0% to 100%).
Decimal, Fraction, Percent Forms: Probability can be expressed in decimal (rounded to 3 decimals), fraction (simplified), or percent (nearest tenth).

Standard Deck of Cards

A standard deck has 52 cards divided into 4 suits with 13 cards each.
Contains a total of 12 face cards (3 per suit).

Theoretical vs. Experimental Probability

Theoretical Probability: Calculated using favorable outcomes divided by total possible outcomes.
Experimental Probability: Determined by the ratio of successful outcomes to the number of trials conducted.

Independent and Dependent Events

Independent Events: The occurrence of one event does not influence another; formula: P(A and B) = P(A) x P(B).
Dependent Events: One event affects another; formula: P(A and B) = P(A) x P(B|A).

Complementary Events

Probability of the Complement of an Event: A̅ = 1 - P(A), where A̅ is the complement of event A.

Joint and Marginal Frequencies

Joint Frequency: The value in each cell of a two-way table.
Marginal Frequency: The sum of rows and columns in a table indicating totals.
Conditional Relative Frequency: Relationship between joint and row totals (joint relative frequency divided by row total).

Overlapping and Mutually Exclusive Events

Overlapping Events: Events that may occur simultaneously; P(A) + P(B) - P(A and B) = P(A or B).
Disjoint Events: Events that cannot happen at the same time; P(A) + P(B) = P(A or B).

Probability Examples

Examples illustrate real-world applications, such as determining probabilities of drawing specific cards from a deck or calculating conditional probabilities based on consumer behavior.

Combinations and Permutations

Permutation: Arrangement of objects where order is important. Example: Arranging the letters in "JUNE."
Combination: Selection of objects where order does not matter. Example: Choosing side dishes or songs.

Factorials and Arrangements

Factorial: Product of an integer and all positive integers below it; represents total arrangements.
Examples of arrangements: Calculating how many orders students can finish in races or how many ways songs can be played.

Probability Distribution

A function providing the probabilities for all possible values of a random variable; total probability must equal 1.

Binomial Distribution

Formulated for scenarios with two possible outcomes (success or failure), characterized by the number of trials (n) and the probability of success (P).

Specific Example Calculations

Binomial example: Survey of dentist visits with probabilities calculated for up to 5 selected adults. The most likely outcome indicated that 3 out of 5 adults had visited a dentist in the last year.

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Description

Test your knowledge of geometric concepts related to probability with these flashcards from Chapter 12. Learn important terms like sample space and outcome, and practice calculating probabilities of events. These flashcards are a perfect tool for mastering key ideas in geometry and probability.