1. Two events are independent if

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 4E: Let E and F be events in a sample space S. aThe probability of E and F occurring is...
icon
Related questions
icon
Concept explainers
Question

fill in the blank

Independent and Mutually Exclusive Events

3.2 Independent and Mutually Exclusive Events
1. Two events are independent if
2. So, two events A and B are independent if one of the following identities is true
formula (2.1)
formula (2.2)
Note that the formula (2.2) can be derived from formula (1.1) and formula (2.1).
3. If two events are NOT independent, then we say that they are dependent.
4. The concept of independent events explains why P({HH}) = P({HT}) = P({TH}) = P({TT})
1/4 for the experiment of tossing two fair coins. Challenge yourself to explain it!
5. with replacement and without replacement
• When an experiment for a probability is to select some members (or a sample) from a set,
there are two ways to conduct the experiment: selecting members one by one with replacement
and selecting them without replacement. These are different experiments. So, they may result
in different probabilities for the same event.
• Do TRY IT 3.6 (with replacement)
• What if you conduct the experiment of TRY IT 3.6 without replacement? Challenge yourself
to find the probability of getting at least one black card when the experiment is done without
replacement.
6. Mutually Exclusive Events
• A and B are mutually exclusive events if
• When A and B are mutually exclusive, P(A And B) :
• A simplest example. For the experiment of tossing a fair coin, the two events {H} and {T} are
mutually exclusive.
• If it is not known whether A and B are mutually exclusive, assume they are not until you can
show otherwise.
Do all examples in the textbook.
Transcribed Image Text:3.2 Independent and Mutually Exclusive Events 1. Two events are independent if 2. So, two events A and B are independent if one of the following identities is true formula (2.1) formula (2.2) Note that the formula (2.2) can be derived from formula (1.1) and formula (2.1). 3. If two events are NOT independent, then we say that they are dependent. 4. The concept of independent events explains why P({HH}) = P({HT}) = P({TH}) = P({TT}) 1/4 for the experiment of tossing two fair coins. Challenge yourself to explain it! 5. with replacement and without replacement • When an experiment for a probability is to select some members (or a sample) from a set, there are two ways to conduct the experiment: selecting members one by one with replacement and selecting them without replacement. These are different experiments. So, they may result in different probabilities for the same event. • Do TRY IT 3.6 (with replacement) • What if you conduct the experiment of TRY IT 3.6 without replacement? Challenge yourself to find the probability of getting at least one black card when the experiment is done without replacement. 6. Mutually Exclusive Events • A and B are mutually exclusive events if • When A and B are mutually exclusive, P(A And B) : • A simplest example. For the experiment of tossing a fair coin, the two events {H} and {T} are mutually exclusive. • If it is not known whether A and B are mutually exclusive, assume they are not until you can show otherwise. Do all examples in the textbook.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Conditional Probability, Decision Trees, and Bayes' Theorem
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage