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Questions and Answers
Mutually exclusive events don’t ______, i.e., P(A and B) = 0
Mutually exclusive events don’t ______, i.e., P(A and B) = 0
overlap
Events are ______ if the probability of one does not affect the probability of the other.
Events are ______ if the probability of one does not affect the probability of the other.
independent
The multiplication rule states P(A and B) = P(A)P(B) if A and B are ______.
The multiplication rule states P(A and B) = P(A)P(B) if A and B are ______.
independent
The addition rule states P(A or B) = P(A) + P(B) – P(A and ______).
The addition rule states P(A or B) = P(A) + P(B) – P(A and ______).
In a bag containing 3 pink gumballs, 5 orange gumballs, and 2 blue gumballs, the sample space is ______.
In a bag containing 3 pink gumballs, 5 orange gumballs, and 2 blue gumballs, the sample space is ______.
The probability of drawing a pink or an orange gumball is ______.
The probability of drawing a pink or an orange gumball is ______.
When drawing two gumballs without replacement, the total number of elements in the sample space is ______.
When drawing two gumballs without replacement, the total number of elements in the sample space is ______.
The probability of drawing a pink gumball on your second draw given that you first drew an orange gumball is ______.
The probability of drawing a pink gumball on your second draw given that you first drew an orange gumball is ______.
The probability of getting a sum of ______ when rolling two dice is 1/36.
The probability of getting a sum of ______ when rolling two dice is 1/36.
The sum of all probabilities in a probability distribution should equal ______.
The sum of all probabilities in a probability distribution should equal ______.
In the survey, the total number of individuals surveyed is ______.
In the survey, the total number of individuals surveyed is ______.
The probability of selecting someone who is ______ 25 years old is 0.3857.
The probability of selecting someone who is ______ 25 years old is 0.3857.
The probability of being a ______ student majoring in Business given that the student is male is 0.52142857.
The probability of being a ______ student majoring in Business given that the student is male is 0.52142857.
The total number of females surveyed in college majors is ______.
The total number of females surveyed in college majors is ______.
If a student is a male and majors in Business, the probability is ______ 0.23183391.
If a student is a male and majors in Business, the probability is ______ 0.23183391.
The events B (majoring in Business) and M (male) are ______ based on the calculations.
The events B (majoring in Business) and M (male) are ______ based on the calculations.
The sample space of tossing a single coin is S={H, ______}
The sample space of tossing a single coin is S={H, ______}
The sample space of tossing two coins is S={______, HT, TH, TT}
The sample space of tossing two coins is S={______, HT, TH, TT}
The sample space of tossing three coins contains ______ elements.
The sample space of tossing three coins contains ______ elements.
The probability of getting heads on both coins when flipping two coins is ______.
The probability of getting heads on both coins when flipping two coins is ______.
If 5% of computers will malfunction, the probability that a computer will ______ is 0.95.
If 5% of computers will malfunction, the probability that a computer will ______ is 0.95.
The probability of rolling a 5 on a single dice roll is ______.
The probability of rolling a 5 on a single dice roll is ______.
The highest probability possible of an event is ______.
The highest probability possible of an event is ______.
The probability of rolling a 5 or less on a single dice roll is ______.
The probability of rolling a 5 or less on a single dice roll is ______.
The probability of picking a pink gumball first and then an orange gumball second is ______.
The probability of picking a pink gumball first and then an orange gumball second is ______.
The probability of drawing 3 aces from a standard deck without replacement is ______.
The probability of drawing 3 aces from a standard deck without replacement is ______.
When drawing a spade first and then a heart, the probability is ______.
When drawing a spade first and then a heart, the probability is ______.
The probability of drawing 6 cards with none being a queen is ______.
The probability of drawing 6 cards with none being a queen is ______.
In a litter of 4 puppies, the probability that all 4 are male is ______.
In a litter of 4 puppies, the probability that all 4 are male is ______.
The probability of rolling a 6 three times in a row on a 6-sided die is ______.
The probability of rolling a 6 three times in a row on a 6-sided die is ______.
The events A and B are impossible to be mutually exclusive because their probabilities exceed ______.
The events A and B are impossible to be mutually exclusive because their probabilities exceed ______.
Assuming events A and B are independent, the calculated probability of both events occurring is ______.
Assuming events A and B are independent, the calculated probability of both events occurring is ______.
Flashcards
Sample Space
Sample Space
A list of all possible outcomes of an experiment.
Probability
Probability
The chance of a specific event occurring.
Probability Formula
Probability Formula
The probability of an event happening is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability Sum
Probability Sum
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Probability of an Impossible Event
Probability of an Impossible Event
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Probability of a Certain Event
Probability of a Certain Event
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Probability of the Complement
Probability of the Complement
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Probability of Independent Events
Probability of Independent Events
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P(A|B)
P(A|B)
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Probability of drawing a specific color gumball
Probability of drawing a specific color gumball
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Probability of drawing two gumballs without replacement
Probability of drawing two gumballs without replacement
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Multiplication Rule
Multiplication Rule
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Addition Rule
Addition Rule
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Independent Events
Independent Events
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Probability of an event
Probability of an event
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Probability of two independent events
Probability of two independent events
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Probability of 'at least one'
Probability of 'at least one'
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Probability of 'either event'
Probability of 'either event'
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Mutually Exclusive Events
Mutually Exclusive Events
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Conditional Probability
Conditional Probability
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Marginal Probability
Marginal Probability
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Joint Probability
Joint Probability
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Independence of Events
Independence of Events
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Contingency Table
Contingency Table
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Sum of Probabilities
Sum of Probabilities
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Study Notes
Module 2 - Probability
- Probability concepts include playing cards, dice, coins, drawing marbles from bags, and online virtual generators. Links are provided for cards, dice, coins, and urns.
Part 1: Terminology and Basics of Probability
-
Sample Spaces: Listing possible outcomes for events.
- Tossing a single coin: S = {H, T}
- Tossing two coins: S = {HH, HT, TH, TT}
- Tossing three coins: S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
- Drawing one marble from a bag with 3 red, 2 green, 5 yellow marbles: S = {R, G, Y}
-
Probabilities: Calculating likelihoods of specific outcomes.
- Probability of getting heads on both coins when flipping two coins: ¼ or 0.25
- Probability of getting exactly 2 heads when flipping three coins: 3/8 or 0.375
- Probability of not getting a tail when flipping three coins: 1/8 or 0.125
- Probability of rolling a 5 on a single die: 1/6 or 0.16667
- Probability of rolling a 5 or less on a single die: 5/6 or 0.8333
- Probability of an event occurring: The lowest is 0 (impossible), the highest is 1 (certain).
Part 2: Compound Events, Conditional Probability, and Independence
- Mutually Exclusive Events: Events that cannot occur together (e.g., P(A and B) = 0).
- Independent Events: The probability of one event does not affect the probability of another (e.g., P(A and B) = P(A) * P(B)).
- Multiplication Rule: Calculating probabilities of compound events.
- Addition Rule: Calculating the probability of either of two events occurring.
Part 3: Additional Examples
- Probability Calculations: Illustrative examples of probability calculations using a standard deck of cards, drawing multiple cards, or different events. Examples of probabilities include drawing 3 aces from a standard deck and drawing a spade and then a heart.
- Probability of Rolling a Number: Calculate probability of rolling a specific number repeatedly on a six-sided die.
- Independent vs. Dependent Events: Determining whether events are independent or dependent and defining them based on factors.
- Probability of Specific Outcome: Defining the probability of a specific outcome given different conditions and rules.
Part 4: Contingency Tables
- Contingency Tables: Analyzing data in tables. Examples include analyzing customer preferences for sandwich shops, the association between two variables, or specific probabilities.
- Calculating Probabilities: Determining probabilities from contingency tables.
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Description
Test your understanding of mutual exclusivity, event independence, and probability rules with this quiz. Covering essential concepts like sample space and probability distributions, this quiz is perfect for 10th-grade students. See how well you grasp the fundamental principles of probability!
