Probability 7 th Grade CCGPS

Lesson 1

Probability Vocabulary Probability – a measure between 0 and 1 to quantify likelihood for processes that have uncertain outcomes; can be expressed as a fraction, decimal or percent. – A probability of “0” means an outcome has a 0% chance of happening – A probability of “1” means that the outcome will happen 100% of the time – A probability of “1/2” means that an outcome is equally likely or unlikely to happen

Probability Vocabulary Sample Spaces – a list of the individual outcomes that are to be considered; their probabilities sum to 1 Probability Model – a probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. Uniform Probability Model – a probability model which assigns equal probability to all outcomes

Types of Probability Uniform Probability – probability that is based on knowing all of the equally likely outcomes. – P(event) = Number of favorable outcomes Total number of outcomes

Finding Uniform Probability Example 1 Find the probability of randomly choosing a blue marble from the marbles shown. P(event) = Number of favorable outcomes Total number of outcomes P(blue) – There are 3 blue marbles There are 10 marbles in all Solution: The probability of choosing a blue marble is 3/10, 0.3, or 30%

Uniform Probability Example 2 In the change pouch of your wallet you have the following coins: 3 pennies, 2 nickels, 4 dimes and 1 quarter. Without looking you randomly choose a coin, what is the probability you will choose a nickel?

Uniform Probability Example 3 In the change pouch of your wallet you have the following coins: 3 pennies, 2 nickels, 4 dimes and 1 quarter. Without looking you randomly choose a coin, what is the probability you will choose a silver coin?

Finding Uniform Probability Your Turn… Find the probability of randomly choosing a green marble. Find the probability of getting “tails” when you flip a coin. Find the probability of getting a “5” when you roll a number cube.

Sample Spaces - Example 1 Determine the SAMPLE SPACE for randomly choosing each color of marble shown. ( Remember a sample space is a list of the individual outcomes that are to be considered; their probabilities sum to 1) – Blue – Red – Green

Sample Spaces - Example 2 In the change pouch of your wallet, you have the following coins: 3 pennies, 2 nickels, 4 dimes and 1 quarter. Determine the sample space for randomly choosing each type of coin. – Penny – Nickel – Dime – Quarter

Sample Spaces – Your Turn Using the spinner shown, determine the sample space for the spinner landing on each color.

Lesson 2

Types of Probability Experimental Probability – probability that is based on repeated trials of an experiment. (Each trial in which the event occurs is a success) – P(event) = Number of success Number of Trials

Finding an Experimental Probability Example 1 A cat that knows the shake commands offers either of its front paws to shake. The table shows the number of times the cat offers each of its paws when asked to shake. What is the likelihood that the cat will offer it right paw when asked to shake? P(right paw) = = 12 Successes 50 Trials Simplify Solution: 6/25, 0.24, or 24%

Experimental Probability Example 2 A game spinner was spun 500 times. The results of the spins are shown in the table below. What is the probability that the spinner will land on A? A128 B267 C105

Finding Experimental Probability Your Turn… What is the probability that the cat will offer its left paw when asked to shake? Of over 20 voters polled after an election for class president, 14 of the voters voted for Sean. What is the probability that a randomly chosen voter voted for Sean?

Sample Spaces and Experimental Probability Consider example 1 – – A cat that knows the shake commands offers either of its front paws to shake. The table shows the number of times the cat offers each of its paws when asked to shake. – Determine the sample space for each of the outcomes.

Sample Spaces and Experimental Probability Consider example 2 – A game spinner was spun 500 times. The results of the spins are shown in the table below. – Determine the sample space for each of the possible outcomes in the table. A128 B267 C105

Lesson 3

Vocabulary Tree Diagram – are useful for describing relatively small sample spaces and computing probabilities, as well as for visualizing why the number of outcomes can be extremely large. Event – any collection of outcomes of an experiment. Compound Events – any events which consists of more than one outcome. Two-Way Table – is a useful tool for examining relationships between categorical variables

Making a Tree Diagram Example 1 You are ordering a fruit smoothie. You have your choice of a small, medium, or large smoothie, and you can include one of the following fruits: strawberries, bananas, or oranges. How many different choices of smoothies do you have? Solution: There are 9 different choices of smoothies

Making a Tree Diagram – Example 2 You will be attending two sessions at a science camp. At each session, you will be assigned to one of the following groups: red, green, blue, or yellow. If you will not be assigned to the same group for both sessions, how many group assignments are possible? Hint: Because you cannot be in the same group for both sessions, do not include the same group in both sessions in the tree diagram. Answer: There are 12 possible group assignments

Your Turn – Making a Tree Diagram You decide to get popcorn at a movie theater. The popcorn comes in regular, large, and jumbo sizes, and you have your choice of plain or buttered popcorn. How many choices of popcorn do you have?

Using a Tree Diagram – Example 1 To find the probability of getting at least 2 heads when tossing a coin 3 times, make a tree diagram to find the outcomes. Answer: Because 4 of the 8 outcomes have at least 2 heads, the probability is 4/8, or ½.

Using a Tree Diagram – Example 2 You are choosing an outfit. You can choose a T-shirt (T), a button-down shirt (B), or a sweater (S) as a top and jeans (J), dress pants (D) or khakis (K) for pants. Make a tree diagram to determine the number of possible outfits you could make.

Example 2 Continued Let’s find the probability that the outfit you choose will have khaki pants in it. Now find the probability that the outfit you choose will the sweater and jeans.

Making and Using a Tree Diagram Your Turn … You are getting ready to make a sandwich for lunch. You can choose a tuna, ham, roast beef or egg salad sandwich and rye, white,wheat or multi-grain bread. First create a tree diagram and them use the outcomes to determine the probability that you will choose your sandwich to be on multi- grain bread.

Lesson 4

Creating a Two-Way Table Example 1 A two-way table is another way to display the outcomes of compound events. The question from the previous slide about outfits can be displayed in a two-way table: T-ShirtButton-DownSweater Jeans Khakis Dress pants

Using a Two-Way Table Let’s complete this two-way table and then determine the probability that the outfit you choose will have jeans in it. T-ShirtButton-DownSweater Jeans Khakis Dress pants

Using a Two-Way Table You can also determine sample spaces from a two-way table as with the other probability models. What would the sample space for outfit situation look like? T-ShirtButton-DownSweater Jeans Khakis Dress pants

Your Turn - Using a Two-Way Table You roll a number cube and flip a coin. What is the probability that you get a 3 and tails?