Probability This material is made freely available at www.njctl.org - PDF document

Slide 1 / 176 Slide 2 / 176 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative Probability This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course 2012-05-05 materials to parents, students and others. www.njctl.org Click to go to website: www.njctl.org Slide 3 / 176 Slide 4 / 176 PROBABILITY Click on a topic to · Introduction to Probability go to that section. · Experimental and Theoretical Introduction to · Word Problems Probability · Fundamental Counting Principle · Permutations and Combinations · Probability of Compound Events · Probabilities of Mutually Exclusive and Overlapping Events Click to go to · Complementary Events Table of Contents This notebook appears in both Pre-Algebra and Algebra. Slide 5 / 176 Slide 6 / 176 Probability Probability Example: What is the probability of flipping a nickel and the · Another way to express probability is to use a nickel landing on heads? fraction. Pull Pull Step 1: What are the possible outcomes? Number of favorable outcomes Step 2: What is the number of favorable outcomes? Probability This number becomes = Pull Pull your numerator. of an event Total number of P = possible outcomes Step 3: Put it all together to answer the question. The probability of flipping a nickel and landing on heads is: 1 . 2

Slide 7 / 176 Slide 8 / 176 1 Arthur wrote each letter of his name on a separate Probability can be expressed in many forms. For example, card and put the cards in a bag. What is the the probability of flipping a head can be expressed as: probability of drawing an A from the bag? 1 or 50% or 1:2 or .5 2 A 0 Need a hint? B 1/6 Probability = Number of favorable outcomes Move the box. Total number of possible outcomes C 1/2 D 1 A R T H U R The probability of randomly selecting a blue marble can be expressed as: 1 or 1:6 or 16.7% or .167 6 Slide 9 / 176 Slide 10 / 176 3 Matt's teacher puts 5 red, 10 black, and 5 green markers 2 Arthur wrote each letter of his name on a separate in a bag. What is the probability of Matt drawing a red card and put the cards in a bag. What is the marker? probability of drawing an R from the bag? A 0 A 0 Probability = Number of favorable outcomes Need a hint? B 1/6 B 1/4 Total number of possible outcomes Move the box. C 1/3 C 1/10 D 1 D 10/20 A R T H U R A Probability = Number of favorable outcomes Need a hint? Total number of possible outcomes Move the box. Slide 11 / 176 Slide 12 / 176 4 What is the probability of rolling a 5 on a fair number 5 What is the probability of rolling an odd on a fair cube? number cube?

Slide 13 / 176 Slide 14 / 176 6 What is the probability of rolling a 7 on a fair number 7 If you have 3 black t-shirts and 4 blue t-shirts, what is cube? the probability of picking a black t-shirt without looking? Slide 15 / 176 Slide 16 / 176 9 Mary chooses an integer at random from 1 to 6. What is the 8 If you enter an online contest 4 times and at the probability that the integer she chooses is a prime number? time of drawing its announced there were 100 total entries, what are your chances of winning? A B C D From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011. Slide 17 / 176 Slide 18 / 176 10 Each of the hats shown below has colored marbles placed inside. Hat A Determine the fewest number of marbles, if any, and the color of these marbles contains five green marbles and four red marbles. Hat B contains six blue that could be added to each hat so that the probability of picking a green marble marbles and five red marbles. Hat C contains five green marbles and five blue will be one-half in each of the three hats. marbles. If a student were to randomly pick one marble from each of these three hats, Hat A contains five green marbles and four red marbles. determine from which hat the student would most likely pick a green marble. Hat B contains six blue marbles and five red marbles. Justify your answer. Hat C contains five green marbles and five blue marbles. Hat A Hat B Hat C Hat A Hat B Hat C From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011 From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011

Slide 19 / 176 Slide 20 / 176 Click on an object. What is the outcome? Experimental & Theoretical Probability Click to go to Outcomes are the different results Table of Contents O u t c o m e that can occur. Slide 21 / 176 Slide 22 / 176 Experimental Probability Experimental Probability Probability number of times the outcome happened Example 1 - Golf of an event number of times experiment was repeated A golf course offers a free game to golfers who make a hole-in-one on the last hole. Last week, 24 out of 124 Flip the coin 5 golfers achieved this. Find the experimental probability that times and a golfer makes a hole-in-one on the last hole. Answers determine the experimental probability of # of successes = 24 heads. = P(hole-in-one) = 124 # of trials 6 Pull Pull The ratio of the number of Experimental 31 times an event occurs to the Probability Heads Tails total number of times that the Out of 31 golfers, you could expect 6 to make a activity is performed. hole-in-one on the last hole. Or there is a 19% chance of a golfer making a hole-in-one on the last hole. Slide 23 / 176 Slide 24 / 176 Experimental Probability Sally rolled a die 10 times and the results are shown below. Example 2 - Surveys Of the first 40 visitors through the turnstiles at an Use this information to answer the following questions. amusement park, 8 visitors agreed to participate in a survey being conducted by park employees. Find the experimental probability that an amusement park visitor # on Die Picture of Roll Results will participate in the survey. 1 1 one # of successes = 8 = 1 2 3 twos P(participation) = # of trials 40 5 3 1 three You could expect 1 out of every 5 people to 4 0 fours participate in the survey. Or there is a 20% chance of a 5 4 fives visitor participating in the survey. 6 1 six

Slide 25 / 176 Slide 26 / 176 What is the experimental probability of rolling a 5? What is the experimental probability of rolling a 4? 11 12 A 1/2 A 1/2 # on Die Picture of Roll Results # on Die Picture of Roll Results 1 1 one 1 1 one B B 5/4 5/4 2 3 twos 2 3 twos C C 4/5 4/4 3 1 three 3 1 three D D 2/5 0 4 0 fours 4 0 fours 5 4 fives 5 4 fives 6 1 six 6 1 six Slide 27 / 176 Slide 28 / 176 Based on the experimental probability you found, if you 13 14 Mike flipped a coin 15 times and it landed on tails 11 times. rolled the die 100 times, how many sixes would you expect What is the experimental probability of landing on heads? to get? # on Die Picture of A Roll Results 6 sixes 1 1 one B 10 sixes 2 3 twos C 12 sixes 1 D 3 60 sixes three 0 4 fours 5 4 fives 6 1 six These are the results after 10 rolls of the die Slide 29 / 176 Slide 30 / 176 Theoretical Probability Theoretical Probability Probability Probability Probability E q u Probability a l l y L i k e l y number of favorable outcomes What is the theoretical of an event total number of possible outcomes Theoretical probability of spinning Probability green? Pull the tabs for definitions. Answer Fair

Slide 31 / 176 Slide 32 / 176 Theoretical Probability Theoretical Probability Example 2 - Marbles Example 1 - Marbles Suppose you randomly choose a gray marble. Find the probability of randomly choosing a Find the probability of this event. white marble from the marbles shown. 3 # of favorable outcomes P(gray) = = # of favorable outcomes 4 2 = # of possible outcomes 10 = P(white) = # of possible outcomes 10 5 There is a 3 in 10 chance of picking a gray There is a 2 in 5 chance of picking a white marble or a 30% possibility. marble or a 40% possibility. Slide 33 / 176 Slide 34 / 176 Theoretical Probability What is the theoretical probability of picking a 15 green marble? Example 3 - Coins Find the probability of getting tails when you flip a coin. A 1/8 7/8 B # of favorable outcomes 1 = P(tails) = 2 # of possible outcomes 1/7 C 1 There is a 1 in 2 chance of getting tails when D you flip a coin or a 50% possibility. Slide 35 / 176 Slide 36 / 176 What is the theoretical probability of picking a What is the theoretical probability of picking a 16 17 black marble? white marble? A 1/8 A 1/8 7/8 7/8 B B 1/7 1/7 C C 1 1 D D