Probability

1. Probability

2. Lesson 6.2.1 Probability California Standard: Statistics, Data Analysis, and Probability 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1–P is the probability of an event not occurring. What it means for you: You’ll learn about using probability as a way to describe how likely events are to happen. • Key words: • probability • chance • likely • percent • fraction • decimal

3. Essential Questions: Why is probability useful in everyday life? Make a connection to other content areas also explore probability?

4. What are the chances that I will roll a six? Probability A lot of the time, you can’t say for sure whether or not one particular event will happen. But you can often say how good the chances are. Probability is a way of using numbers to describe the chance of an event happening.

5. Vocabulary Probability is a way of using numbers to describe the chance of an event happening. Event- When we say "Event" we mean one (or more) outcomes that are possible. Example Events: Getting a Tail when tossing a coin is an event

6. “What is the probability it will snow today?” “How likely is it that the school football team will win its next game?” “What is the chance that you will go to a movie this weekend?” Very unlikely Certain Impossible Fairly unlikely Even chance Quite likely Very likely Probability Some Events Are More Likely to Happen Than Others People often talk about things that might happen, using words like “chance,”“likely,” and “probability”: Look at the line below and think about where your answer would be for each of these questions.

7. Very unlikely Certain Impossible Fairly unlikely Even chance Quite likely Very likely Probability Guided Practice Decide where you would put the chances of the following events happening on this scale: 1. Leaves falling from the trees next fall. 2. Finding a live elephant in your bedroom when you get home. 3. Winning a raffle if you have 1 out of 100 tickets. Certain Very very unlikely Very unlikely Solution follows…

8. Very unlikely Certain Impossible Fairly unlikely Even chance Quite likely Very likely Probability Guided Practice Decide where you would put the chances of the following events happening on this scale: 4. Winning a raffle if you have 99 out of 100 tickets. 5. Winning a raffle if you have 1 out of 1,000,000 tickets. 6. A tossed coin landing on heads. Very likely Very very unlikely Even chance Solution follows…

9. Probability Guided Practice 7. Put the events named in Exercises 1–6 in order, from most likely to least likely. • Leaves falling from the trees next fall. • Finding a live elephant in your bedroom when you get home. • Winning a raffle if you have 1 out of 100 tickets. • Winning a raffle if you have 99 out of 100 tickets. • Winning a raffle if you have 1 out of 1,000,000 tickets. • A tossed coin landing on heads. Most likely Least likely 1 4 6 3 5 2 Solution follows…

10. Very unlikely Certain Impossible Fairly unlikely Even chance Quite likely Very likely or 50% 0 or 0% 1 or 100% 1 2 Probability Probability Is a Way to Say How Likely an Event Is In math, probability is a way of describing the chance that an event will occur. Probability can be written using fractions, decimals, or percents. You can replace the words on the line below with numbers that represent how likely an event is to occur:

11. 0% 50% 100% 1 A probability of (or 50%) means that the event might happen, but there’s anequal chance that it won’t. 0 1 2 1 2 Lesson 6.2.1 Probability A probability of 0 (or 0%) means that there is no chance. A probability of 1 (or 100%) means that the event will definitely happen.

12. Lesson 6.2.1 Probability Guided Practice Estimate the probability that each of the following things will happen. Write your answers as percents. 8. It will go dark tonight. 9. Your math teacher will turn into a pineapple. 10. A 6th-grader from California chosen at random will be a girl. 100% 0% About 50% Solution follows…

13. 1 5 0 10 2 8 25 10 0 25 10 10 Probability Guided Practice Use the list of probabilities below to answer Exercises 11–12. 11. Which of the probabilities above represents an impossible event? 12. Which of the probabilities above represents a certain event? Solution follows…

14. Probability Probability Is Usually Calculated Exactly There are many situations where you can say exactlywhat the probability of an event is. This isn’t the same as saying whether an event willdefinitely (or not definitely) happen — it’s just a measure of how likely the event is.

15. Probability Example 1 What is the probability of spinning the color red on this spinner? What is the probability of spinning the color blue? Solution Spinning the color red is certain, so the probability is 1. Spinning the color blue is impossible, so the probability is 0. Solution follows…

16. = 0.25 = 25% 1 4 Probability Example 2 What is the probability of spinning the color blue on this spinner? Solution The blue section is one-fourth of the spinner. So the probability of spinning the color blue is If you spun the spinner lots of times, about one-fourth of the spins would land on blue. Solution follows…

17. Probability Guided Practice Exercises 13–15 are about this spinner. Find the probability of spinning the colors below. Write your answers as decimals. 13. Blue 14. Yellow 15. Pink Half the spinner is blue, so the probability of spinning blue is one-half or 0.5. Half the spinner is yellow, so the probability of spinning yellow is one-half or 0.5. It is impossible to spin pink, so the probability is 0. Solution follows…

18. 1 1 1 4 3 5 Probability Guided Practice In Exercises 16–18, find the probability of spinning the color yellow on each of the following spinners. Write your answers as fractions. 16. 17. 18. Solution follows…

19. A. B. C. D. For each set of cards, find the probability of picking: 1. a triangle card 2. a star card A: B: C: D: A: B: C: D: 1 1 1 2 1 5 4 5 4 5 Probability Independent Practice Each set of cards shown below is turned over and shuffled, then one card is picked. 0 0 1 Solution follows…

20. 1 1 1 4 4 2 Probability Independent Practice A bag has 1 red, 1 blue, and 2 yellow marbles in it. 3. How many marbles are in the bag? 4. How many marbles are red? What is the probability of drawing a red marble? 5. How many marbles are blue? What is the probability of drawing a blue marble? 6. How many marbles are yellow? What is the probability of drawing a yellow marble? 4 1 1 2 Solution follows…

21. 0.375 375% 0.375% 37.5% % 3 3 8 8 0.55 55 11 100 100 20 Probability Independent Practice 7. The probability of an event occurring is . Which two values below represent this same probability? 8. The probability of an event occurring is 55%. Which two values below represent this same probability? 55 5.5 Solution follows…

22. 3 5 Probability Independent Practice 9. In a tiled hallway, kids are jumping from one tile to the next. The probability of landing on a green tile is 60%. What fraction of the hallway area is covered with green tiles? Solution follows…

23. Probability Round Up Probability is useful because you can use it to compare the chances of different events happening. The event with the highest probability is the most likely to occur.