13-1 representing sample spaces
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13-1 Representing Sample Spaces. You calculated experimental probability. . Use lists, tables, and tree diagrams to represent sample spaces. Use the Fundamental Counting Principle to count outcomes. Experiments, Outcomes, and Events. - PowerPoint PPT PresentationTRANSCRIPT
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13-1 Representing Sample Spaces
You calculated experimental probability.
• Use lists, tables, and tree diagrams to represent sample spaces.
• Use the Fundamental Counting Principle to count outcomes.
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Experiments, Outcomes, and Events
The sample space of an experiment is the set of all possible outcomes.Tree diagram is an organized table of line segments (branches) which shows possible experiment outcomes.
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One red token and one black token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Represent the sample space for this experiment by making an organized list, a table, and a tree diagram.Organized List Pair each possible outcome from the first drawing with the possible outcomes from the second drawing.R, R B, BR, B B, R
Table List the outcomes of the first drawing in the left column and those of the second drawing in the top row.
Tree Diagram
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One yellow token and one blue token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Choose the correct display of this sample space.
A. B.
C. D. Y, Y; B, B; Y, B
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Experiment Stages
Two-stage experiment – an experiment with two stages or events (like the 1st problem).Multi-stage experiment – experiments with more than two stages.
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Multi-Stage Tree DiagramsCHEF’S SALAD A chef’s salad at a local restaurant comes with a choice of French, ranch, or blue cheese dressings and optional toppings of cheese, turkey, and eggs. Draw a tree diagram to represent the sample space for salad orders.
The sample space is the result of 4 stages.● Dressing (F, R, or BC)● Cheese (C or NC)● Turkey (T or NT)● Eggs (E or NE)Draw a tree diagram with 4 stages.
Answer:
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A. 3
B. 4
C. 5
D. 6
BASEBALL GAME In the bleachers at a major league game you can purchase a hotdog, bratwurst, or tofu dog. This comes with the optional choices of ketchup, mustard, onions, and/or relish. How many stages are in the sample space?
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The Fundamental Counting Principle
• If you have 2 events: 1 event can occur m ways and another event can occur n ways, then the number of ways that both can occur is m*n
• Event 1 = 4 types of meats• Event 2 = 3 types of bread
• How many different types of sandwiches can you make?
• 4*3 = 12
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p. 917
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3 or more events:
• 3 events can occur m, n, & p ways, then the number of ways all three can occur is m*n*p
• 4 meats• 3 cheeses• 3 breads• How many different sandwiches can you
make?• 4*3*3 = 36 sandwiches
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• At a restaurant at Cedar Point, you have the choice of 8 different entrees, 2 different salads, 12 different drinks, & 6 different deserts.
• How many different dinners (one choice of each) can you choose?
• 8*2*12*6=• 1152 different dinners
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Use the Fundamental Counting Principle
CARS New cars are available with a wide selection of options for the consumer. One option is chosen from each category shown. How many different cars could a consumer create in the chosen make and model?
Use the Fundamental Counting Principle.exterior interior seat engine computer wheels doors possiblecolor color outcomes11 7 5 3 6 4 3 83,160 × × × × × × =
Answer: So, a consumer can create 83,160 different possible cars.
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A. 3,888
B. 3,912
C. 4,098
D. 4,124
BICYCLES New bicycles are available with a wide selection of options for the rider. One option is chosen from each category shown. How many different bicycles could a consumer create in the chosen model?
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13-1 Assignment
p. 918, 6-8, 15-18, 20