1. Probability
The branch of mathematics that describes the pattern of chance outcome.

2. Chapter 6 Probability: The Study of Randomness
Probability calculations are the basis for inference.
You can make predictions, describe trends, etc. using probability.
You ask the question “How often would this method give me the correct answer if I used it very many times?”

3. BIG IDEA
Chance behavior is unpredictable in the short run BUT has a regular and predictable pattern in the long run.
(MANY, MANY, MANY repetitions)
Did I mention MANY?

4. Spinning Pennies We will spin a penny 50 times…
What do you think the probability is of spinning a penny?
Write your guess in the blank on your half sheet.
Find a partner and run the activity while filling out the half sheet and graph (each person will spin 50 times).
OUR GOAL? Estimate the probability of spinning a head.

5. The assignment was to SPIN a penny 50 times and record the number of heads and tails. As class we recorded _____ trials and the class average was _____. Why do you think this is?

6. 6.1 The Idea of Probability
What does it mean to say that a probability of a fair coin is one half, or that the chances I pass this class are 80 percent, or that the probability that the Panthers win the Super Bowl this season is .1?
A probability is a numerical measure of the likelihood of the event. It is a number that we attach to an event.

7. Probability Of An Event P(A) = The Number Of Ways Event A Can Occur
We call a phenomenon RANDOM if individual outcomes are uncertain, but there is a regular distribution of outcomes in a larger number of repetitions.
Probability Of An Event P(A) = 
The Number Of Ways Event A Can Occur   
The Total Number Of Possible Outcomes

8. Randomness
You must have a long series of independent trials. (one outcome does not influence the outcome of any other)
The idea of probability is empirical. (based on observation rather than theory)
Short runs only give estimates, computer simulations are very useful so to be able to do LONG RUN of simulations.

9. DO #’s 2,4

10. #6.2
I did 20 simulations of randint(0,1,4) and recorded the number of times Betty won or loss {-4,-2,0,2,4}.
My simulation outcomes were 1/20 (-4), 6/20 (-2), 5/20 (0), 8/20 (2), 0/20 (4).
What were yours?

11. # 6.4 A) 0 is the probability for an impossible event
B) 1 is the probability for an event that is certain.
C) .01 is the probability for an event that is very unlikely.
D) 0.6 is the probability that an event will occur more often than not.

12. The sample space S of a random phenomenon is the set of all possible outcomes.
Example: If the experiment is to throw a standard die and record the outcome, the sample space is S = {1, 2, 3, 4, 5, 6}, the set of possible outcomes.

13. Techniques for finding the number of outcomes:
Tree Diagram – represent the first action, then draw “branches” to the next set of actions.
Multiplication Principle (of Counting) – do one task in “a” number of ways and another task in “b” number of ways, then both tasks can be done in “a” x “b” ways.

14. Work with your partner DO #11,14
Be complete and concise with your answers.
Do them NOW! 

15. Probability Rules The probability of an event is written P(A).
The complement, P(AC)= 1-P(A).
Events A and B are disjoint or mutually exclusive if the have no outcomes in common.
P(A or B)= P(A) + P(B) (addition rule)
Events A and B are independent if
P(A and B)= P(A)P(B).

16. #11 A) S = { germinates, fails to grow}
B) S = { 1,2,3,…..} depending on if you measure in days, weeks, months.
C) S = { A,B,C,D,F}
D) S = {HHHH, HHHM, HHMH, HMHH, MHHH, HHMM, HMHM, MMHH, MHMH, MHHM, HMMH, MMMH, MMHM, MHMM, HMMM, MMMM}
E) S = {4,3,2,1,0}

17. #14 P(at least one head)=? A) 2 x 2 = 4 S = {hh, ht, th, tt}
B) 2 x 2 x 2 = 8
S = {hhh, hht, hth, thh, tth, tht, htt, ttt}
C) 2 x 2 x 2 x 2 = 16
{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, TTHH, THTH, THHT, HTTH, TTTH, TTHT, THTT, HTTT, TTTT}
P(at least one head)=?

18. Examples The probability of choosing each color of a peanut m&m is
P(Blue)=
P(Brown U Red)=
P(Yellowc)=

19. Homework
Read and Take notes 6.2
Do #’s 3,5,12,15,18,19,21,23,26,30