12.8 independent and dependent events
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The document discusses dependent and independent events and probabilities. It provides examples of calculating probabilities for dependent and independent compound events using formulas like P(A and B) = P(A) x P(B) for independent events. It also uses tree diagrams to calculate probabilities for scenarios involving multiple events like the probability of rain on different days.
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Independent and dependent events notes
1) Independent events are events where the outcome of one event does not affect the outcome of the next event. Dependent events are events where the outcome of the first event affects the probability of the outcome of the second event.
2) The probability of two independent events occurring is calculated by multiplying the individual probabilities. The probability of two dependent events occurring factors in how the first event affects the probability of the second.
3) Examples are provided to demonstrate calculating probabilities of independent and dependent events, such as spinning spinners or drawing marbles from a bag.
union and intersection of events.ppt
The document discusses probability and events, defining key terms like experiment, outcome, sample space, and event. It provides examples of simple and compound events, and explains how to calculate the probability of simple events using the formula of number of outcomes in the event over the total number of possible outcomes. Rules for probability are also outlined, such as the probability of any event being between 0 and 1 and the sum of probabilities of all outcomes equaling 1.
Probability of Simple and Compound Events
This document contains a lesson plan on probability for students. It begins with definitions of key probability terms and examples of calculating probabilities of simple and compound events. It then provides word problems for students to practice calculating probabilities. The document concludes with additional practice problems for students to answer. The overall document provides instruction and practice on fundamental concepts in probability.
Introduction of Probability
This document defines key concepts in probability, including experiments, outcomes, sample spaces, events, unions and intersections of events, complements of events, mutually exclusive events, and the probability of independent and dependent events. It provides examples to illustrate these concepts, such as calculating the probability of drawing cards from a deck or marbles from a box. Formulas are given for calculating probabilities of unions, intersections, complements, mutually exclusive and inclusive events.
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Identify whether events are independent or depdendent
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Independent and dependent events notes
1) Independent events are events where the outcome of one event does not affect the outcome of the next event. Dependent events are events where the outcome of the first event affects the probability of the outcome of the second event.
2) The probability of two independent events occurring is calculated by multiplying the individual probabilities. The probability of two dependent events occurring factors in how the first event affects the probability of the second.
3) Examples are provided to demonstrate calculating probabilities of independent and dependent events, such as spinning spinners or drawing marbles from a bag.
union and intersection of events.ppt
The document discusses probability and events, defining key terms like experiment, outcome, sample space, and event. It provides examples of simple and compound events, and explains how to calculate the probability of simple events using the formula of number of outcomes in the event over the total number of possible outcomes. Rules for probability are also outlined, such as the probability of any event being between 0 and 1 and the sum of probabilities of all outcomes equaling 1.
Probability of Simple and Compound Events
This document contains a lesson plan on probability for students. It begins with definitions of key probability terms and examples of calculating probabilities of simple and compound events. It then provides word problems for students to practice calculating probabilities. The document concludes with additional practice problems for students to answer. The overall document provides instruction and practice on fundamental concepts in probability.
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This document defines key concepts in probability, including experiments, outcomes, sample spaces, events, unions and intersections of events, complements of events, mutually exclusive events, and the probability of independent and dependent events. It provides examples to illustrate these concepts, such as calculating the probability of drawing cards from a deck or marbles from a box. Formulas are given for calculating probabilities of unions, intersections, complements, mutually exclusive and inclusive events.
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Identify whether events are independent or depdendent
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This document provides an introduction to probability. It defines probability as a numerical index of the likelihood that a certain event will occur, with a value between 0 and 1. It discusses examples of using probability terms like chance and likelihood. It also covers key probability concepts such as experiments, outcomes, events, and sample spaces. It explains different types of probability including subjective, objective/classic, and empirical probabilities. It provides examples of calculating probabilities of events using various approaches.
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To find the probability of two independent events:
1. Find the probability of each individual event
2. Multiply the probabilities together
To find the probability of two dependent events:
1. Find the probability of the first event
2. Find the probability of the second event given that the first event occurred
3. Multiply the probabilities together
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This document provides a lesson on conditional probability that includes:
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probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in
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12.8 independent and dependent events 1
The document discusses dependent and independent events and probabilities. It provides examples of dependent vs independent events, such as drawing cards from a deck with or without replacement. It also shows how to calculate probabilities of compound events using the multiplication rule for independent events and directly for dependent events.
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probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in mathematics 10 .statistics and probability . probability of a mutually and non mutually events. topic in
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(7) Lesson 9.7
To determine the probability of two independent events occurring:
1. Find the probability of each individual event. For example, if spinning a spinner with four equal sections and rolling a six-sided die, the probability of each event would be 1/4 and 1/6 respectively.
2. Multiply the probabilities of the individual events. Since independent events do not influence each other, we can treat them as separate occurrences.
3. The product of the individual probabilities is the probability the two independent events will both occur. Continuing the spinner and die example, the probability of a specific outcome on the spinner AND a specific outcome on the die is (1/4) × (1/6) = 1/
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Lesson 11 5 b notes dependent & independent events
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- 4. Dependent & Independent Events Section 12. 8
- 9. GUIDED PRACTICE for Examples 1and 2 In Exercises 1 and 2 , tell whether the events are independent or dependent. Explain your reasoning. 1. You toss a coin. Then you roll a number cube. You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles. 2. The coins toss does not affect the roll of a dice, so the events are independent. ANSWER There is one fewer number in the bag for the second draw, so the events are dependent. ANSWER
- 11. EXAMPLE 2 Standardized Test Practice The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss resulting in a win. So the probability of each event is . 1 25 ANSWER The probability of two winning tosses in a row is . 625 1 The correct answer is A . P ( win and win ) = P ( win ) P ( win ) 25 1 1 25 =
- 12. GUIDED PRACTICE for Examples 1and 2 3. You toss a coin twice. Find the probability of getting two heads. P ( head and head ) = P ( head ) P ( head ) = 1 4 or 25% 1 2 1 2 = The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss ANSWER
- 13. Daily Homework Quiz For use after Lesson 12. 8 5/10 x 4/9 2. A bag contains ten cards numbered 1 through 10 . You pick one card and then another without replacement. What is the probability that both cards display a value of 6 or higher? ANSWER 2 9 – , 0.2
- 14. Daily Homework Quiz For use after Lesson 12. 8 1. Events A and B are independent. P(A & B) = P(A) x P(B) P (A) 0.75 , P (B) 0.5 , P (A and B) _____ ANSWER 0.75 x 0.5 = 0.375
- 15. Daily Homework Quiz For use after Lesson 12. 8 1. Events A and B are dependent. P(A & B) = P(A) x P(B) P (A) 0.75 , P (B given A) _?_ , P (A and B) 0.3 ANSWER 0.3 ÷ 0.75 = 0.4
- 17. Lesson 12.8 , For use with pages 694-700 2. You choose an M or P. 1. You choose an O. You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the ODDS . 1 3 = ANSWER 3 5 ANSWER 2 6
- 19. Dependent & Independent Events Section 12. 8
- 21. EXAMPLE 3 Finding Probability of Dependent Events Bingo SOLUTION You need B 7 and N 44 for bingo. Find the probability of success when each of the next 2 numbers is drawn. Then multiply. You are playing the bingo card shown. The caller has 50 numbers left to call. What is the probability that you will get bingo with the next 2 numbers called?
- 22. EXAMPLE 3 Finding Probability of Dependent Events P ( B 7 or N 44) There are 50 numbers left to call. Multiply the probabilities. There are 49 numbers left to call. = 1 25 P ( remaining number ) = 1 49 P ( both numbers ) = 1 25 1 49 = 1225 1 ANSWER The probability that you will get bingo when the next 2 numbers are called is, or about 0.0008 . 1225 1 2 50 =