Please prepare your “Blocking Lab”

Please prepare your “Blocking Lab” Make sure it includes name of each group member and the “follow up” questions.

Agenda • Warm Up – Finalize the Blocking Lab • HW Check #2,3,4,5,8 (5 – 10 minutes) • Chapter 6.1 (5 minutes) • Activity (15 – 20 minutes) • Class work problems (15 – 20 minutes) • Assign Homework

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

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?”

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?

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 .4? • A probability is a numerical measure of the likelihood of the event. It is a number that we attach to an event.

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

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.

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.

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.

Going over homework • Read #2 p334 • What are all the possible outcomes? We need to understand THIS first in order to do this problem. • Outcomes: • { -4, -2, 0, 2, 4 }

#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?

#6.3 Randint (0,1,100) stor L1 (easier than naming SHAQ) Let’s do this on the calculator

# 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.

#6.5 I counted 21 zero’s in the RDT in the back of the book; what did you get? Therefore the proportion of 0’s in our RDT is 21/200 or .105 which is very close to our expected probability of .1

#6.8 The probability of being dealt “3 of a kind” in a 5 card poker hand is 1/50. What does this mean in simple language? To me this means that I am favored to get a “3 of a kind” in 1 out of 50 hands of 5 card poker.

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 flat, non tilted surface and run the activity while filling out the half sheet and graph. • OUR GOAL? Estimate the probability of spinning a head.

Classwork • Once done with the Spinning Pennies, turn in your work (make sure you have done your plot). • DO #11,14, be complete and concise with your answers. Do them NOW!  • If you get done, start your homework: • Read and Take notes 6.2 • Do #’s12,15,18,19,21,23,26,30

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?

#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}

#14 • 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}

Homework • Read and Take notes 6.2 • Do #’s12,15,18,19,21,23,26,30

Please prepare your “Blocking Lab”