Independent Events Independent events are two events in which the occurrence of one has no effect on the probability of the other.

Slides:



Advertisements
Similar presentations
Holt Algebra Independent and Dependent Events 11-3 Independent and Dependent Events Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation.
Advertisements

Revision Sheet 1.
AP Statistics Probability.
PROBABILITY OF INDEPENDENT AND DEPENDENT EVENTS SECTION 12.5.
Probability : Combined events 2
 Probability- the likelihood that an event will have a particular result; the ratio of the number of desired outcomes to the total possible outcomes.
Bellwork What fraction of the spinner is blue? Write in simplest form.
EXAMPLE 4 Find a conditional probability Weather The table shows the numbers of tropical cyclones that formed during the hurricane seasons from 1988 to.
Section 2 Probability Rules – Compound Events Compound Event – an event that is expressed in terms of, or as a combination of, other events Events A.
Independent and Dependent Events
Warm-Up 1. What is Benford’s Law?
Conditional Probability The probability that event B will occur given that A will occur (or has occurred) is denoted P(B|A) (read the probability of B.
9-4 Theoretical Probability Theoretical probability is used to find the probability of an event when all the outcomes are equally likely. Equally likely.
Warm-Up A woman and a man (unrelated) each have two children .
Warm Up Tyler has a bucket of 30 blocks. There are
7th Probability You can do this! .
Lesson 3-6. Independent Event – 1st outcome results of probability DOES NOT affect 2nd outcome results Dependent Event – 1st outcome results of probability.
List one thing that has a probability of 0?. agenda 1) notes on probability 2) lesson 1 example 1, 2 Exercise 5-8 Problem set 1-3 3)start lesson 3.
Math I.  Probability is the chance that something will happen.  Probability is most often expressed as a fraction, a decimal, a percent, or can also.
Math I.  Probability is the chance that something will happen.  Probability is most often expressed as a fraction, a decimal, a percent, or can also.
Warm Up Multiply. Write each fraction in simplest form. 1. 2.  Write each fraction as a decimal
Probability.
Math 30-2 Probability & Odds. Acceptable Standards (50-79%)  The student can express odds for or odds against as a probability determine the probability.
Lesson 3-6. Independent Event – 1st outcome results of probability DOES NOT affect 2nd outcome results Dependent Event – 1st outcome results of probability.
Discrete Math Section 16.2 Find the probability of events occurring together. Determine whether two events are independent. A sack contains 2 yellow and.
Chapter 10 – Data Analysis and Probability 10.8 – Probability of Independent and Dependent Events.
CHAPTER 15 PROBABILITY RULES!. THE GENERAL ADDITION RULE Does NOT require disjoint events! P(A U B) = P(A) + P(B) – P(A ∩ B) Add the probabilities of.
0-11 Probability Goal: Find the probability of an event occurring. Eligible Content: A
Independent and Dependent Events Lesson 6.6. Getting Started… You roll one die and then flip one coin. What is the probability of : P(3, tails) = 2. P(less.
Independent and Dependent events. What is the difference between independent and dependent events?  You have three marbles in a bag. There are two blue.
Chapter 7 Review Problems. Problem #1 Use a Venn diagram and the given information to determine the number of elements in the indicated region. n(A) =
Probability is the study of the chance of events happening. A probability can be expressed as a fraction, decimal, or a percent. Experimental Probability.
Question 1 Q. Four cards are drawn from a pack of 52 cards. Find the probability of, 1. They are King, Queen, Jack, & Ace 2. First is King, then Queen,
2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Chapter 9.
MATHPOWER TM 12, WESTERN EDITION Chapter 8 Probability 8.2A 8.2A.1.
CH 22 DEF D: Tables of Outcomes E: Compound Events F: Tree Diagrams.
Classifying Events 8.2A Chapter 8 Probability 8.2A.1
Warm Up 1. Two coins are tossed. What is the probability of getting two heads? 2. Give the probability that the roll of a number cube will show 1 or 4.
Please copy your homework into your assignment book
An Introduction to Probability Theory
Aim: What is the multiplication rule?
PROBABILITY Probability Concepts
Chapter 11 Probability.
1.4 Non-Mutually- Exclusive (1/4)
LEARNING GOAL The student will understand how to calculate the probability of an event.
Learn to find the theoretical probability of an event.
Probability of Multiple Events
13.4 – Compound Probability
Independent and Dependent Events
Lesson 13.4 Find Probabilities of Compound Events
Lesson 11.8 – 11.9 Compound Probability
The probability of event P happening is 0. 34
P(A and B) = P(A) x P(B) The ‘AND’ Rule
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Agenda 1).go over lesson 6 2). Review 3).exit ticket.
Warm Up There are 5 blue, 4 red, 1 yellow and 2 green beads in a bag. Find the probability that a bead chosen at random from the bag is: 1. blue 2.
Compound Probability.
Two Way Frequency Tables
Conditional Probability
Addition and Multiplication Rules of Probability
video WARM-uP Lesson 33 + brain break Exit card
Mutually Exclusive Events
12.5 Find Probabilities of (In)dependent Events
Station #1 Tell whether the events are independent or dependent. Explain why.
Addition and Multiplication Rules of Probability
Probabilities of Compound Events
Note 6: Conditional Probability
Applied Statistical and Optimization Models
Presentation transcript:

Independent Events Independent events are two events in which the occurrence of one has no effect on the probability of the other.

Dependent Events Dependent events are two events in which the occurrence of one changes the probability of the other.

Carl Dick Heather Ellen Alan Greg

Probability of Dependent Events If A and B are dependent events, then P(A and B) = P(A) x P(B|A).

Probability of Dependent Events P(B|A) is read as “probability of B given A.”

Example 1 Select a name from the box and then select a second name without replacing the first. Find the probability of drawing a boy’s name followed by a girl’s name.

B = Select a boy’s name. G|B = Select a girl’s name, given that a boy’s name was selected on the first draw. 4 6 = 2 3 = 2 5 = P(B) P(G|B) P(B and G) = P(B) x P(G|B) 2 3 = x 2 5 4 15 = ≈ 0.27

Example 2 A bag of chocolate candies contains ten brown, eight orange, three yellow, and four green candies. What is the probability that the first two candies drawn from the bag without replacement will be brown?

B = Select a brown candy. B|B = Select a brown candy, given that a brown was already selected. 10 25 = 2 5 = 9 24 = 3 8 = P(B) P(B|B) P(B and B) = P(B) x P(B|B) 2 5 = x 3 8 3 20 = = 0.15

Example The names of ten club members, four boys and six girls, are placed in a hat. Jack is one of the boys and Sally is one of the girls. Suppose that the first name drawn will be the president and the second will be the vice-president.

Example Are the events independent or dependent? dependent

Example Find P(Jack, then a boy). 1 30

Example Find P(a girl other than Sally, then a boy). 2 9

Example Find P(a boy, then a girl). 4 15

Example Find P(a girl, then a boy). 4 15

Example What is the probability that one boy and one girl will be selected? 8 15

1 2 4 3

Probability of Independent Events If A and B are independent events, then P(A and B) = P(A) x P(B).

Example 3 Find P(4 and tails). 1 4 5 2

Find P(4 and tails). 2 6 = 1 3 = 1 2 = P(4) P(T) P(4 and T) = P(4) x P(T) 1 3 = 1 2 1 6 = ≈ 0.17

Example 4 A three-digit number is to be formed by drawing one of four slips of paper with the digits 1, 2, 3, and 4 from a hat. The first draw determines the first digit of the number to be formed, and so on.

Example 4 Digits can be used more than once, so the digit drawn is replaced in the hat before the next draw. What is the probability that the three-digit number formed is 123?

Find P(1 and 2 and 3). P(1 and 2 and 3) = P(1) x P(2) x P(3) 1 4 = x x 1 64 = ≈ 0.016

Example The names of ten club members, four boys and six girls, are placed in a hat. Jack is one of the boys and Sally is one of the girls. Suppose names will be drawn to select a boy’s representative and a girl’s representative.

Example Are the events independent or dependent? independent

Example What is the probability that Jack and Sally will be chosen as the representatives? 1 24

Example What is the probability that neither Jack nor Sally will be chosen? 5 8

Example What is the probability that Sally will be chosen but Jack will not? 1 8

Exercise In a Christian high school of 250 students, 92 play only the piano, 12 play only the trumpet, and 8 play both.

Exercise Use a Venn diagram to help you find the probability that each of the following will occur. Express your answer as both a fraction and a decimal rounded to the nearest thousandth.

Exercise Find the probability that a student drawn at random plays the trumpet. 2 25 = 0.08

Exercise Find the probability that a student drawn at random plays the piano. 2 5 = 0.4

Exercise Find the probability that a student drawn at random plays the piano and the trumpet. 4 125 = 0.032

Exercise Find the probability that a student drawn at random plays the piano, given that he plays the trumpet. 2 5 = 0.4

Exercise Does P(plays the piano and the trumpet) = P(plays the piano, given that he plays the trumpet)? no