PROBABILITY UNIT
General Education Mathematics
INSTRUCTIONAL
MEDIA
THE FUNDAMENTAL COUNTING PRINCIPAL
INTERNET VIDEOS
http://www.youtube.com/watch?v=qJ7AYDmHVRE 6:33 min., tree diagrams, the fundamental
counting principal, The last example of the fundamental counting principal is also known as what?
(a permutation)
http://www.youtube.com/watch?v=aaLFtI1YgKM 10:43 min., tree diagrams, the fundamental
counting principal, What do students often forget to use when counting digits? (the zero – there
are 10 digits)
PENCASTS
License plate fundamental counting principal problem 11.1.19
PROFESSOR SHOTS LECTURES
Two fundamental counting principal problems
WRITING
ASSIGNMENTS
1. Solve a problem using both a tree diagram and the Fundamental Counting Principle. Describe
one advantage of using the Fundamental Counting Principle rather than a tree diagram.
COLLABORATIVE & 1. Write and solve an original problem that can be solved using the Fundamental Counting
CRITICAL PROBLEM
Principle.
SOLVING
INSTRUCTIONAL
MEDIA
PERMUTATIONS AND FACTORIAL NOTATION
INTERNET VIDEOS
http://www.youtube.com/watch?v=JyRKTesp6fQ 10:54 min., permutations, factorial notation,
repetitive or indistinguishable items, using TI84+, If using factorial notation, “n” must be what
type of number? (a whole number)
PENCASTS
Permutations and duplicates 11.2.55
PROFESSOR SHOTS LECTURES
Permutations, factorial notation, duplicate items
WRITING
ASSIGNMENTS
1. Explain the best way to evaluate
900 !
without using a calculator.
899 !
2. If 24 permutations can be formed using the letters in the word BAKE, why can’t 24
permutations also be formed using the letters in the word TATE? How is the number of
permutations in TATE determined?
COLLABORATIVE & 1. Write and solve a word problem that can be solved by evaluating 5!
CRITICAL PROBLEM
SOLVING
COMBINATIONS
INSTRUCTIONAL
MEDIA
INTERNET VIDEOS
http://www.youtube.com/watch?v=uATuM3ajhBw 9:56 min, combinations using factorial
notation with 3 word problem examples, “And” statements indicate what? (mulitiply)
PENCASTS
Combination committee problem 11.3.57
WRITING
ASSIGNMENTS
PROFESSOR SHOTS LECTURES
Combinations and the difference between combinations and permutations
1. Explain how to distinguish between permutation and combination problems.
2. To open a combination lock, you must know the lock’s three-number sequence in its proper
order. Repetition of numbers is permitted. Why is this lock more like a permutation lock than
a combination lock? Why is it not a true permutation problem? (The order is important. Since
the numbers may be repeated, it is not a true permutation lock)
COLLABORATIVE & Write and solve a word problem that can be solve by evaluating 7C3 .
CRITICAL PROBLEM
SOLVING
PROBABILITY INTRODUCTION
INSTRUCTIONAL
MEDIA
INTERNET VIDEOS
http://www.khanacademy.org/math/applied-math/cryptography/crypt/v/probability-space 2:48
minutes, basic probability explained well – event/sample space In the lecturers exact words, how
do you calculate the probability of a random event, such as a dice roll? (You divide the number of
ways that event can occur by all possible outcomes.)
http://www.youtube.com/watch?v=YWt_u5l_jHs 7:53 sample space, event, theoretical and
empirical probability, complement, (What is another way of saying the probability of the
complement of an event or E(P’)? (E prime)
PENCASTS
Probability basics die problem 11.4.37
PROFESSOR SHOTS LECTURES
Theoretical & Empirical probability problems
WRITING
ASSIGNMENTS
1. Describe the difference between theoretical probability and empirical probability.
2. Give an example of an event whose probability must be determined empirically rather than
theoretically.
3. Use the definition of theoretical probability to explain why the probability of an event that is
certain to occur is 1.
COLLABORATIVE & 1. List the possible outcomes from a roll of two die
CRITICAL PROBLEM
Find the probability of getting: two even numbers, two numbers who sum is 5, then 7. Now
SOLVING
actually roll the die 50 times recording the outcomes. Find the empirical probabilities of the
above.
2. Color Chips; Each team has a bag of 20 chips.
Taking turns, without looking into the bag, remove a chip and record the color. Repeat 40
times, finding the empirical probability of getting each color.
Now look at all the chips and determine the theoretical probability of each color. Discuss the
difference.
3. A driver approaches a toll booth and randomly selects two coins from his pocket. If
the pocket contains two quarters, two dimes, and two nickels, what is the probability
that the two coins he selects will be at least enough to pay a thirty-cent toll?
4. Let’s Make a Deal – Monty Hall Problem using cups not curtains
Demonstrate in front of class having the students decide.
Use a shell game – one ball under one of three cups.
Select a cup. One cup without the ball is removed. Ask; switch or keep your original choice?
Have students simulate the game 15 times. Put a ball under one cup, choose a cup, ask to
switch, then reveal the choice. Carefully record the events. Now answer the original question.
Is it better to switch or stick with your original choice? Why? (2/3 probability when switching)
http://www.khanacademy.org/math/probability/independent-dependentprobability/dependent_probability/v/monty-hall-problem Monty Hall problem explained
PROBABILITY and Counting (The Fundamental Counting Principle, Permutations & Combinations)
INSTRUCTIONAL
INTERNET VIDEOS
MEDIA
http://www.youtube.com/watch?v=exCkDy1ducM&feature=youtu.be 5:42 minutes, Shows one
example of using the fundamental counting theorem to find the probability, We can use the
fundamental counting theorem or think of it as a _____ (permutation) since the order matters.
http://www.youtube.com/watch?v=mR7MjU-tAC4&feature=youtu.be 6:43 minutes, Shows two
examples of using permutations to find the probability, Q: Probability can be expressed by a
___(decimal) and ____(percentage) as well.
http://www.youtube.com/watch?v=MKq9AdWhDtM&feature=youtu.be 7 minutes; Uses both the
calculator and hand calculation to find probability using combinations, Q: On the calculator E – 7
means ___(times 10 to the -7).
http://www.youtube.com/watch?v=s5PVpJGCo5Y&feature=youtu.be 8:37minutes; Uses both the
calculator and hand calculation to find probability using combinations with groups (the counting
principle), Q: We know it has to be a combination because ____(order) doesn’t matter.
PENCASTS
Using combinations to find probability 11.5.17
PROFESSOR SHOTS LECTURES
Using the Fundamental Counting Principal, permutations & combinations to find probability
WRITING
ASSIGNMENTS
COLLABORATIVE & Of 100 persons in a company, 70 are married, 80 are college graduates, and 60 are both married
CRITICAL PROBLEM and college graduates. Find the probability that if a person is selected at random from this group,
SOLVING
the person will be; Married and a college graduate (3/5), married or a college graduate (9/10), not
married and not a college graduate (1/10).
INSTRUCTIONAL
MEDIA
PROBABILITY using Complement Rules
http://www.youtube.com/watch?v=7oDkPOE-Fek&feature=youtu.be 4:31 minutes, Uses the
complement rules to find probability, Q: Not > is the same as ___(less than or equal to).
PROFESSOR SHOTS LECTURES
Finding the probability of an event not occurring, mutually exclusive and not mutually exclusive
events, odds
WRITING
ASSIGNMENTS
COLLABORATIVE &
CRITICAL PROBLEM
SOLVING
PROBABILITY (“OR” MUTUALLY EXCLUSIVE EVENTS)
INSTRUCTIONAL
MEDIA
http://www.youtube.com/watch?v=zxhDOvS2c3k&feature=youtu.be 4:09 minutes, Shows two
examples of finding probability of mutually exclusive events, Q: If events A and B are mutually
exclusive then probability of A or B is equal to the ____(probability of a plus the probability of B).
PENCASTS
Using “or”, mutually exclusive events to find probability 11.6.21
WRITING
ASSIGNMENTS
PROFESSOR SHOTS LECTURES
Use previous lecture
1. Give an example of events that are mutually exclusive.
2. Explain how to find “or” probabilities with mutually exclusive events. Give an example.
COLLABORATIVE &
CRITICAL PROBLEM
SOLVING
INSTRUCTIONAL
MEDIA
WRITING
ASSIGNMENTS
PROBABILITY (“OR” NOT MUTUALLY EXCLUSIVE EVENTS)
http://www.youtube.com/watch?v=z-1VvourLsA&feature=youtu.be 6:41 minutes, Shows two
examples of finding probability of not mutually exclusive events, Q: The reason we need to
___(subtract) from our probability is because we counted some twice.
http://www.youtube.com/watch?v=bHQoOPAgcpM 6:11 minutes, Shows how to find the
probability of the union U of two events (basically not mutually exclusive events), Q: In
determining the probability of two events, we may be counting successful outcomes ___(twice).
PENCASTS
PROFESSOR SHOTS LECTURES
Use previous lecture
1. What is the difference between mutually exclusive and not-mutually exclusive events? Give
an example of each.
2. Explain how to find “or” probabilities with events that are not mutually exclusive. Give an
example.
COLLABORATIVE &
CRITICAL PROBLEM
SOLVING
INSTRUCTIONAL
MEDIA
ODDS
http://www.youtube.com/watch?v=76XEBRaelD0&feature=youtu.be 3:57 minutes, Defines and
gives two examples of finding odds using probability, Q: The odds in favor of an event is a ratio of
the number of ___(favorable) ways to the number of ______(unfavorable) says.
PENCASTS
Find odds 11.6.83
WRITING
ASSIGNMENTS
COLLABORATIVE &
CRITICAL PROBLEM
SOLVING
PROFESSOR SHOTS LECTURES
Use previous lecture
Explain how to find the odds in favor of an event if you know the probability that the event will
occur.
INSTRUCTIONAL
MEDIA
INDEPENDENT & DEPENDENT EVENTS
http://www.khanacademy.org/math/probability/independent-dependentprobability/dependent_probability/v/independent-events-1
2:39 minutes, Explains the
difference between independent and dependent events, Q: If you replace the item it is ____
(independent event) and if you do not replace the item it is ___(dependent event).
http://www.youtube.com/watch?v=xgoQeRyvw5I 8:05 minutes, Explains how to find the
probability of independent events with 2 examples, Q: Events are independent if the outcome of
one event does not affect the ___(outcome) of the other event.
http://www.khanacademy.org/math/probability/independent-dependentprobability/dependent_probability/v/introduction-to-dependent-probability
6:38
minutes,
dependent events introduced (without replacement), When you are trying to determine whether
or not you should play a game (how much you may/may not win) what must you find?
WRITING
ASSIGNMENTS
PROFESSOR SHOTS LECTURES
Independent & dependent events, conditional probability
Explain how to find “and” probabilities with independent events. Give an example.
What is the difference between independent and dependent events? Give an example of each.
Explain how to find “and” probabilities with dependent events. Give an example.
COLLABORATIVE &
CRITICAL PROBLEM
SOLVING
INSTRUCTIONAL
MEDIA
CONDITIONAL PROBABILITY
http://www.youtube.com/watch?v=u03NipAbyYg 7:52 minutes; Defines and gives 4 conditional
probability problems using the formula and basic probability definition, Q: Why would you want
to use the formula instead of the basic probability definition? (if you are given probabilities rather
than circumstances to worth with)
PENCASTS
Conditional Probability 11.7.52
PROFESSOR SHOTS LECTURES
See previous lecture
WRITING
ASSIGNMENTS
COLLABORATIVE &
CRITICAL PROBLEM
SOLVING
INSTRUCTIONAL
MEDIA
EXPECTED VALUE
http://www.youtube.com/watch?v=UVl9CQcBNt8 8:03 minutes, Explains and shows 2 ways how
to figure the expected value of playing a game, Q: What is the expectation or the____ (average
long range pay out) of playing the game.
PENCASTS
Finding expected value of a game 11.8.15
PROFESSOR SHOTS LECTURES
Expected value of a game
WRITING
ASSIGNMENTS
1. How do insurance companies use expected value to determine what to charge for a policy?
2. Describe a situation in which a business can use expected value.
3. If the expected value of a game is negative, what does this mean?
COLLABORATIVE & Deal or No Deal Game
CRITICAL PROBLEM
SOLVING