Probability and Statistics
Focus: Practical Applications of Statistics
The student will
a) compare and contrast dependent and independent events; and
b) determine probabilities for dependent and independent events. 


Essential Knowledge and Skills 
 Determine whether two events are dependent or independent.
 Compare and contrast dependent and independent events.
 Determine the probability of two dependent events.
 Determine the probability of two independent events.

Essential Understandings 
 How can you determine if a situation involves dependent or independent events? Events are independent when the outcome of one has no effect on the outcome of the other. Events are dependent when the outcome of one event is influenced by the outcome of the other.


Vertical Articulation 
 SOL 4.13ab  a) predict the likelihood of
simple event; b) represent
probability as a number between 0 and 1
 SOL 5.14  make predictions/determine
probability by constructing a sample
space
 SOL 7.9  investigate/describe the
difference between the
experimental/theoretical probability
 SOL 7.10  determine the probability of
compound events, Basic Counting
Principle
 SOL 8.12  determine probability of
indep/dep events with and without
replacement

Instructional Materials 
 VDOE Enhanced Enhanced Scope and Sequence Lesson: It Could Happen (PDF)  Differentiating between dependent and independent events (Word)
 Notes: Probability (flipchart)  15 slides: notes and practice understanding probability including independent and dependent
 Guided Practice: Independent and Dependent Probability Practice Problems (flipchart)  9 practice questions between independent and dependent probability
 VDOE Algebra Readiness Curriculum Companion: Exploring Probability (pdf)

Real World Lessons 

Practice 
 Worksheet: Probability of Simple, Independent, and Dependent Events (pdf)  15 practice problems (simple events are grade 4 review)
 Worksheet: Probability Practice (doc)  3 pages practicing independent and dependent probability
 Worksheet: Independent vs. Dependent Events (pdf)  25 mixed practice problems including word problems

SOL Mini Quiz 
 SOL 6.16 Mini Quiz: Probabilities (pdf)

Skills 
 Mathematics Assessment Project
 A20:Memory Game  Apprentice  In this task, you use probability to find a good strategy for winning a memory game.
 E06:Lottery  Expert  In this task, you must use math to decide whether a lottery idea will make money.

Videos 
 YouTube: Independent and Dependent Probability
 YouTube: Probability of Compound Events
 PH: Finding the probability of a single event

Explore
Learning 
 Compound Independent Events: Compare the theoretical and experimental probabilities of compound independent events by drawing colored marbles from a bag. Record the results of successive draws with replacement of marbles to calculate the experimental probability.
 Compound Independent and Dependent Events: Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
 Spin the Big Wheel! (Probability): Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel.

Websites 
 Math Goodies: Independent Events Notes and Practice
 IXL Math: Probability of Independent and Dependent Events
 BrainGenie: Finding Probabilities

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Exploring Probability  The lessons focus on creating sample spaces and using the Fundamental (Basic) Counting
Principle. Students calculate experimental probability through games and then calculate the theoretical
probability. (pdf)

Common Core
Standards 
SCP.1 
SCP.2 
SCP.3 
7.SP.8a 
7.SP.8b 
SCP.1 
SCP.2 
SCP.3 
SCP.5 
