# Warm-Up. OBJ & DOL  SWBAT determine the probability of a particular event (3.5.a)  Given 2 multiple choice questions and a constructed response, students.

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Warm-Up

OBJ & DOL  SWBAT determine the probability of a particular event (3.5.a)  Given 2 multiple choice questions and a constructed response, students will predict outcomes using theoretical probability with 80% accuracy. ObjectiveDOL

Essential Question  Probability helps us determine how likely things like insurance, lottery tickets and poker hands will work out in our favor.  How can I use probability to find out how likely an event is to happen? WhyEssential Question

Quick Check  3/20  5/16  4/19  14/27  13/34  21/31  43/100  62/75 Write these fractions as decimals (to the nearest hundredth) .15 .31 .21 .52 .38 .68 .43 .83 Write these decimals as percents  15%  31%  21%  52%  38%  68%  43%  83%

Number of favorable outcomes Total number of outcomes Theoretical Probability

Let’s try one…  A letter is selected at random from the word FLORIDA. What is the probability the letter is an A?  Hold up number of favorable outcomes.  Hold up number of possible outcomes.  Write it as a fraction:  Write it as a decimal:  Write it as a percent:

One more…  What is the probability of the spinner landing on an odd number?  Write it as a fraction:  Write it as a decimal:  Write it as a percent: 5 7 8 2

Whiteboards  A number is selected at random from the numbers 1 to 50. Find each probability in a fraction, decimal, and percent. P(multiple of 3)P(a factor of 50) P(not a factor of 50)

Whiteboards  Use the letters M, A, T, H, E, M, A, T, I, C, and S to find each probability. Write each as a fraction, decimal, and percent.  P(M)P(not vowel)P(not E)

Marbles  There are 8 blue marbles, 9 orange marbles, and 6 yellow marbles in a bag. Find the probabilities.  P(blue)  P(not orange)

Think-Write-Pair-Share  What marbles could you add or remove to ensure that the probability of drawing a blue marble is 1/3? Justify your answers with a minimum of 3 complete sentences.

Extension…  What is the probability of the spinner landing on an odd number and landing on heads 5 7 8 2 1/2 Multiply ½ x ½ = ¼

What is the probability of the spinner landing on an odd number and the coin landing on heads? MAKE A TREE DIAGRAM 5 7 8 2 2 7 8 5 Heads Tails Heads Tails Heads Tails Heads Tails 2 out of 8 have an odd then heads Simplify to 1 out of 4 What is this as a percent?

Marbles  There are 8 blue marbles, 9 orange marbles, and 6 yellow marbles in a bag. Find the probabilities, given replacement.  P(blue, then yellow)  P(orange, then blue)

Marbles  There are 8 blue marbles, 9 orange marbles, and 6 yellow marbles in a bag. Find the probabilities, without replacement.  P(blue, then yellow)  P(orange, then blue)

One of these names is to be drawn from a hat, find the probability as a fraction, decimal, and percent. MaryJenny BobMarilyn BillJack JerryTina ConnieJoe

1) P(3-letter name) 2) P(4-letter name) 3) P(name starting with T) 4) P(name starting with S) 5) P(name starting with B) 6) P(name ending with Y) 7) P(7-letter name) 8) P(Name containing 2 N’s) 9) P(Name not starting with J) 10) P(Name not starting with S)

Math that makes you go hmmmmmmm……..  A traditional dice is tossed one time. What is the probability that an even number will be rolled?  P(even) = P(2) + P(4) + P(6)  = 2 + 4 + 6  = 12  Think-Write-Pair-Share: What’s wrong with this logic? Where did the error occur and how would it be corrected?

Experimental probability  Experimental probability is just like theoretical probability except it is based off of data that has already occurred!!!!! Number of successful outcomes Total number of outcomes

Real World Number of Movies Number of Moviegoers More than 7 movies per month 123 5–7 movies per month 133 2–4 movies per month 265 Less than 2 movies per month 226 Total747 What is the probability of a person going to the movies 5-7 times per month?

Real World Number of Movies Number of Moviegoers More than 7 movies per month 123 5–7 movies per month 133 2–4 movies per month 265 Less than 2 movies per month 226 Total747 What is the probability of a person going less than 2 or more than 7 movies per month?

Real World MaleFemale Humanities7080 Science5080 Other6070 First Class of the Day for College Students What is the probability of a person having science as their first class?

Real World MaleFemale Humanities7080 Science5080 Other6070 First Class of the Day for College Students What is the probability of a female having humanities or science first?

Real World MaleFemale Humanities7080 Science5080 Other6070 First Class of the Day for College Students What is the probability of a male not having humanities first?

Probability Review Partner A Explain: THEORETICAL Probability Theoretical probability can be found without doing an experiment. Partner B Explain: EXPERIMENTAL Probability Experimental probability is found by repeating an experiment and observing the outcomes.

The Car Simulation  Each group will have a bag of numbers that represent the number of cars owned by people in Tiny Town.  You will have 15 minutes to complete both the theoretical and experimental probabilities.  Look at the number on the bottom of your worksheet. That is your group number.  Once in your group, send the oldest partner up to get the bag of numbers.

The Car Simulation  Think – Pair - Share  How did your experimental probabilities compare to the theoretical probabilities?  Partner A please stand.  Whip Around  Partner A please share how your experimental probabilities compared to the theoretical probability.

Complement of an Event  Flipping heads on a coin  Drawing a red card  Rolling a 5 on a die  90% chance of snow  Flipping tails on a coin  Drawing a black card  Not rolling a 5 on a die  10% chance it won’t snow EventComplement Based on this, can you come up with a definition for complement of an event?

Complement of an Event  All outcomes that are NOT the event.

Calculating the probability of a complement  What is the probability of flipping heads on a coin?  50%  What is the probability of the complement of this event?  1 -.5 = 50%

Calculating the probability of a complement  A pair of dice are rolled. What is the probability of rolling doubles?  6/36 = 1/6  What is the probability of the complement of this event?  1 – 1/6 = 5/6

Calculating the probability of a complement  A gumball machine contains gumballs of five different colors: 36 red, 44 white, 15 blue, 20 green, and 5 orange. The machine dispenser randomly selects one gumball. What is the probability that the gumball selected is:  One of the colors of the American flag?  95/120 = 19/24  What is the probability of the complement of this event?  1 – 19/24 = 5/24

Summarize the essential question  How can I use probability to find out how likely an event is to happen? TOOLBOX TheoreticalExperimental SuccessfulTotal # OutcomesReplacement

DOL Proficient  a. 1/10  b.1/2  c.5/9  d.2/10  a.5%  b.20%  c.12%  d. 50% A spinner numbered 1 through 10 is spun. Each outcome is equally likely. P(odd) P(even then 2) with replacement

DOL – Advanced Color# Blue13 Green12 Red7 Yellow9 Brown15  P(green)  P(color starting with b)  P(red then brown) with replacement Marbles

DOL #3  What’s the probability of drawing a heart from a deck of 52 playing cards?  What’s the complement of this event and what would the probability of it be?

DOL Proficient  a. 1/10  b.1/2  c.5/9  d.2/10  a.5%  b.20%  c.12%  d. 50% A spinner numbered 1 through 10 is spun. Each outcome is equally likely. P(odd) P(even then 2)with replacement

DOL – Advanced Color# Blue13 Green12 Red7 Yellow9 Brown15  P(green)  P(color starting with b)  P(red then brown) with replacement Marbles

DOL #3  What’s the probability of drawing a heart from a deck of 52 playing cards?  13/52 = ¼ = 25%  What’s the complement of this event and what would the probability of it be?  Complement would be drawing a spade, club, or diamond  ¾ or 75%

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