Mini-Unit. Data & Statistics. Investigation 1: Correlations and Probability in Data

Transcription

1 Mini-Unit Data & Statistics Investigation 1: Correlations and Probability in Data I can Measure Variation in Data and Strength of Association in Two-Variable Data Lesson 3: Probability Probability is a measure of how it is that something is going to happen. Probability can be measured as a or a. When measured as a fraction, it will be between (it is that the event will happen) and (it is that the event will happen). When measured as a percentage, it will be between (it is that the event will happen) and (it is that the event will happen). Events and Outcomes Two words associated with probability are EVENTS and OUTCOMES. Events are what is happening. Outcomes are the results. For example, if someone is tossing a coin, the EVENT is the coin toss. The OUTCOMES are what the results could be: heads or tails. If there was a bag of yellow, green, and red marbles, and someone wanted to determine the probability of selecting a certain color, the EVENT would be selecting a marble. The OUTCOMES would be selecting a yellow marble, selecting a green marble, and selecting a red marble. 1. There is a plate with seven cookies: two peanut butter, two chocolate chip, and three sugar. What would be the event and outcomes if one cookie was selected at random? 2. When playing a bean bag toss game, there are three holes that you could toss your bean bag into. What would be the event and outcomes of this situation?

2 Calculating Probability To determine the probability that something will happen, we need to use. To find the probability, we divide the number of times that an outcome has/could occur by the total number of events/trials/outcomes. Probability = For example, if someone has a coin and they want to determine the probability that if the coin was flipped, it would land on tails, the probability would be 1 (< in one flip,tails is one outcome that could occur) 2 (< in one flip,there are two possible outcomes) If someone had a standard deck of playing cards and they were to select one card at random, what is the probability that they would select a five? How many cards are in a playing deck? How many of those cards are a five? To determine probability, we take the number of chances the outcome has to occur and divide by the total number of outcomes. 1. A bag has 3 yellow crayons, 2 blue crayons, 4 red crayons, and 1 green crayon. If one crayon is selected at random, what is the probability that it will be a yellow crayon? What is the probability that it will be a red or green crayon?

3 is the realistic probability that something will happen. is found by figuring out the number of favorable outcomes divided by the number of total outcomes. Think of as though you had ONE chance to complete an event. Theoretically, what is the probability that a certain outcome would happen? Example: A magician put a rubber ball under one of three cups, mixed the cups around, and now you have to select cup 1, cup 2, or cup 3 to see which cup has the ball. The following chart shows the theoretical probability of each cup Cup 1 1/3 Cup 2 1/3 Cup 3 1/3 The ball can only be under one cup and there is one of each cup. So your favorable outcome is 1. There are three possible outcomes, though: cup 1, cup 2, and cup 3. So your total outcomes is There is a bin of 9 markers: 2 red, 4 pink, 2 purple, and 1 blue. Complete the chart to show the theoretical probability for each marker color if one marker was selected at random. 2. In a bag, there is an assortment of marbles: 3 sparkled marbles, 4 striped marbles, 2 solid color marbles, and 2 clear marbles. Make a chart to show the theoretical probability for each marble type if one marble was selected at random.

4 is found after a series of trials have been completed. The purpose of is to determine what the probability of a specific outcome would be after a series of trials occurred. For example, someone flipped a coin 18 times and recorded their data below. Fill out the chart for the experimental probability of each outcome. #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 H H H T T H T H H T T H H T T H T H Heads (H) Tails (T) 1. A standard six-sided dice was rolled and the results were tracked below. Fill out the chart for the experimental probability of each outcome. Result Rolled Number of Times Rolled With a partner, roll the dice that you are given 30 times. Record the outcome after each roll. Once the 30 trials are completed, create a chart showing the experimental probability of your data.

5 Representing Probability Probability is typically represented as a fraction or percentage. However, it can also be written as a decimal. In Unit 2, you learned how to convert fractions to decimals. In this lesson, you will be applying what you know to convert your probability from a fraction to a decimal and then to a percentage. If I wanted to convert 1 into a decimal, I would complete long division: as a decimal is.25 To change any decimal into a percentage, move the decimal point TWO PLACES to the RIGHT, and then add a percentage sign. 1. Complete the chart for theoretical probability written as a fraction, decimal, and percentage, of a certain color pencil being selected from 1 red, 3 pink, and 2 purple. Outcome as a Fraction as a Decimal as a Percentage 2. With the dice, roll it 10 times and record your data. Create a chart for each outcome (even if a certain number wasn t rolled) and represent the experimental probability for each outcome as a fraction, decimal, and percentage.