Podcast
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 ______).
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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 ______.
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The probability of drawing a pink or an orange gumball is ______.
The probability of drawing a pink or an orange gumball is ______.
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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 ______.
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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 ______.
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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.
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The sum of all probabilities in a probability distribution should equal ______.
The sum of all probabilities in a probability distribution should equal ______.
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In the survey, the total number of individuals surveyed is ______.
In the survey, the total number of individuals surveyed is ______.
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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.
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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.
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The total number of females surveyed in college majors is ______.
The total number of females surveyed in college majors is ______.
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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.
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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.
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The sample space of tossing a single coin is S={H, ______}
The sample space of tossing a single coin is S={H, ______}
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The sample space of tossing two coins is S={______, HT, TH, TT}
The sample space of tossing two coins is S={______, HT, TH, TT}
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The sample space of tossing three coins contains ______ elements.
The sample space of tossing three coins contains ______ elements.
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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 ______.
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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.
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The probability of rolling a 5 on a single dice roll is ______.
The probability of rolling a 5 on a single dice roll is ______.
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The highest probability possible of an event is ______.
The highest probability possible of an event is ______.
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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 ______.
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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 ______.
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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 ______.
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When drawing a spade first and then a heart, the probability is ______.
When drawing a spade first and then a heart, the probability is ______.
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The probability of drawing 6 cards with none being a queen is ______.
The probability of drawing 6 cards with none being a queen is ______.
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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 ______.
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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 ______.
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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 ______.
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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 ______.
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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}
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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!
