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Probability 0011 0010 1010 1101 0001 0100 1011 1 2 4 Corresponds to Chapter 6 in the text “kinda” Basic Probability 0011 0010 1010 1101 0001 0100 1011 • Def: Probability is defined as the ratio of favorable outcomes to total outcomes 1 2 – notation: P(e) = favorable total 4 – What is the probability of flipping a coin and getting a head? Terms 0011 0010 1010 1101 0001 0100 1011 • Sample Space • P(E) 1 2 – between 0 and 1 4 Practice 0011 0010 1010 1101 0001 0100 1011 • Pg 333 (6.1, 6.3, 6.4, 6.8) 1 2 4 Example 1: 0011 0010 1010 1101 0001 0100 1011 • You have six marbles in a jar. There are 2 blue, 3 red, and 1 yellow. What is the 1 2 probability that you reach in the jar and the marble you pull is yellow? 4 Let’s Explore Your Data 0011 0010 1010 1101 0001 0100 1011 • When you flipped a coin, did you always get half to be heads, and half to be tails? 1 2 – Why? 4 Theoretical vs. Experimental 0011 0010 1010 1101 0001 0100 1011 • Theoretical Probability: • Experimental Probability: 1 2 4 – What happened as we did more trials??? Practice 0011 0010 1010 1101 0001 0100 1011 • pg. 340 (6.11, 6.14, 6.18) • Page. 348 (6.19, 6.21, 6.25) 1 2 4 Compound Probability 0011 0010 1010 1101 0001 0100 1011 • And – P( _____ and _______ ) • Or 1 2 4 – P( _____ or ______ ) • Conditional Probability – P ( a b) Terms 0011 0010 1010 1101 0001 0100 1011 • Mutually Exclusive • Independent 1 2 • Dependent • Complement 4 And 0011 0010 1010 1101 0001 0100 1011 • P(A and B)= P(A) * P(B) 1 2 4 Or 0011 0010 1010 1101 0001 0100 1011 • P(A or B)=P(A) +P(B) – P(A and B) 1 2 4 Mutually Exclusive 0011 0010 1010 1101 0001 0100 1011 • P(A and B)=0 • P(A or B)= P(A) + P(B) 1 2 4 Complement 0011 0010 1010 1101 0001 0100 1011 1 2 4 Conditional Probability 0011 0010 1010 1101 0001 0100 1011 • Calculate the probability of a scenario, given _______ has already occurred 1 2 – P ( a b) • The probability of A, given B has occurred. 4 • P ( a b)= P (b a ) P (b) Practice 0011 0010 1010 1101 0001 0100 1011 • pg. 369 (6.54, 6.58, 6.59) 1 2 4 Law of Large Numbers 0011 0010 1010 1101 0001 0100 1011 • The Law of Large Numbers states, the more trials you have, the experimental probability 1 2 should approach the theoretical probability • Activity 1: • Activity 2: 4 Let’s Revisit the Marble Problem 0011 0010 1010 1101 0001 0100 1011 • You have six marbles in a jar. There are 2 blue, 3 red, and 1 yellow. What is the 1 2 probability that you reach in the jar and the marble you pull is yellow? 4 – What if I asked you to pull two marbles…. • P( yellow and blue) P(yellow and blue) • Does the first draw…assuming its yellow, 0011 0010 1010 1101 0001 0100 1011 affect the second. • This is an example of independent events 1 2 – The first outcome does not affect the probability of 4 the second • This is an example of dependent events – The first outcome does affect the outcome of the second probability Activity 4 0011 0010 1010 1101 0001 0100 1011 • To Replace or Not to Replace? 1 2 4 Activity 8 0011 0010 1010 1101 0001 0100 1011 • I’m on a roll! 1 2 4 Back to Theory 0011 0010 1010 1101 0001 0100 1011 • Simulations are great ways of approximating probability. But what chance do I really 1 2 have!! 4 Recall 0011 0010 1010 1101 0001 0100 1011 • Probability is the favorable number of outcomes over the sample space…that’s it! 1 2 4 Example 0011 0010 1010 1101 0001 0100 1011 • Assuming gender is equally likely, what the probability when I have more children I will 1 2 have at least 1more girl. – how many ways can I get 1 more girl? 4 – how many possible outcomes are there? Tree Diagram Example 0011 0010 1010 1101 0001 0100 1011 1 2 4 P ( sum = 5) 0011 0010 1010 1101 0001 0100 1011 1 2 4 Pascal’s Triangle 0011 0010 1010 1101 0001 0100 1011 1 2 4 Next verse…same as the first! 0011 0010 1010 1101 0001 0100 1011 • What is the probability, that in the next two children I have, at least 1 will be a girl. Number of Ways of Girls getting 1 2 Go back to 4 0 Pascal’s Triangle. Find the row with three options! 1 2 Practice 0011 0010 1010 1101 0001 0100 1011 • pg. 364 (6.47, 6.52) • pg. 369 ( 6.58, 6.59) 1 2 4 Permutation 0011 0010 1010 1101 0001 0100 1011 • A way of getting a sample space, when order does not matter. 2 – What is the probability I can randomly open a locker, lock? 1 4 – 1/???? – More ways!!!!—Larger sample space • 123, 321, 213….area all different Combination 0011 0010 1010 1101 0001 0100 1011 • A way of getting a sample space, when order does matter. 1 2 – I have 5 students, I want to choose 2 at a time. How many groups can I choose? – Smaller sample size 4 • Brad and Andrea is the same as Andrea and Brad Combination or Permutation (and solve) 0011 0010 1010 1101 0001 0100 1011 • We are at the singles, tennis championship. There are 5 players, Ryan, Megan , Nicole, 1 2 Justin, and Kyle. Each player must play each other once. How many matches will 4 be held? Combination or Permutation (and solve) 0011 0010 1010 1101 0001 0100 1011 • How many ways different numbers could you choose for the Tennessee Pick 5 Lottery 1 2 (generates numbers 1-38) 4

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