Probability (Counting Principle)
Related Topics:
Common Core for Grade 7
Common Core for Mathematics
More Math Lessons for Grade 7
Examples, solutions, videos, and lessons to help Grade 7 students learn how to find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
A. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
B. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
C. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Common Core: 7.SP.8
Suggested Learning Targets
This video explains how the fundamental counting principle can help you determine the number of possible outcomes or combinations very quickly.
Examples:
1. You flip a coin and spin a spinner. How many outcomes are possible?
2. You pick a marble and roll a die. How many outcomes are possible?
3. Hunter wants to buy a new pair of skates. He can buy speed skated, figure skates, or hockey skates. A pair of skates can come in blue or silver, and can be decorated with blue streaks or green clovers. How many different combinations can Hunter choose from?
The Counting Principle
This video explains how to find the number of ways an event can occur.
Examples:
1. How many ways can students answer a 3 question true or false quiz?
2. How many passwords using 6 digits where the first two digits must be letters and the last four digits must be numbers?
3. A restaurant offers a dinner special in which you get to pick 1 item from 4 different categories.
Beverage: Soda, Tea, Beer, or Wine
Appetizer: Vegetables, Cheese, or Soup
Meal: Veggie burger, Tofu salad, Stir fry egg plant
Dessert: Frozen Yogurt, Cookie, or Brownie
How many different meals are possible?
4. A door lock on a classroom requires entry of 4 digits. All digits must be numbers, but the digits can not be repeated, How many unique codes are possible? Examples of using the fundamental counting principle 1. An apartment complex offers apartments with four different options, designated by A through D.
A: One bedroom, Two bedrooms, Three bedrooms
B: One bathroom, Two bathrooms
C. First floor, Second floor
D: Lake view, Golf course view, No special view
How many apartment options are available? Describe two such options.
2. A car model comes in nine colors, with or without air conditioning, with or without sunroof, with or without automatic transmission, and with or without antilock brakes. In how many ways can the car be ordered with regard to these options?
3. How many different four-letter radio station call letters can be formed if the first letter must be W or K?
4. A social security number contains nine digits. How many security numbers can be formed? How the Fundamental Counting Principle can be used to solve counting problems?
Examples:
1. The school cafeteria offers a choice of two main courses (grilled cheese sandwiches or soup of the day) and five deserts (jello, pudding, fruit cups, sundaes, or granola bars). How many different lunches could you have?
2. John is color blind. He has 5 different pairs of pants, 8 different shirts, 9 pairs of socks varying in color and 3 pairs of shoes. How many different "outfit" can John show up in school in if he must wear pants, socks, a shirt and shoes? Fundamental Counting Principle
Common Core for Grade 7
Common Core for Mathematics
More Math Lessons for Grade 7
Examples, solutions, videos, and lessons to help Grade 7 students learn how to find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
A. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
B. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
C. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Common Core: 7.SP.8
Suggested Learning Targets
- I can explain that the fraction of outcomes in probability of a compound event is similar to the probability of a simple event.
- I can use tree diagrams, frequency tables, and organized lists to determine the probability of a compound event.
- I can identify the outcomes in a sample space.
- I can represent probability outcomes as fractions, decimals, or percents.
- I can design a simulation to estimate the probability of a compound event.
- I can se a simulation to estimate the probability of a compound event.
This video explains how the fundamental counting principle can help you determine the number of possible outcomes or combinations very quickly.
Examples:
1. You flip a coin and spin a spinner. How many outcomes are possible?
2. You pick a marble and roll a die. How many outcomes are possible?
3. Hunter wants to buy a new pair of skates. He can buy speed skated, figure skates, or hockey skates. A pair of skates can come in blue or silver, and can be decorated with blue streaks or green clovers. How many different combinations can Hunter choose from?
This video explains how to find the number of ways an event can occur.
Examples:
1. How many ways can students answer a 3 question true or false quiz?
2. How many passwords using 6 digits where the first two digits must be letters and the last four digits must be numbers?
3. A restaurant offers a dinner special in which you get to pick 1 item from 4 different categories.
Beverage: Soda, Tea, Beer, or Wine
Appetizer: Vegetables, Cheese, or Soup
Meal: Veggie burger, Tofu salad, Stir fry egg plant
Dessert: Frozen Yogurt, Cookie, or Brownie
How many different meals are possible?
4. A door lock on a classroom requires entry of 4 digits. All digits must be numbers, but the digits can not be repeated, How many unique codes are possible? Examples of using the fundamental counting principle 1. An apartment complex offers apartments with four different options, designated by A through D.
A: One bedroom, Two bedrooms, Three bedrooms
B: One bathroom, Two bathrooms
C. First floor, Second floor
D: Lake view, Golf course view, No special view
How many apartment options are available? Describe two such options.
2. A car model comes in nine colors, with or without air conditioning, with or without sunroof, with or without automatic transmission, and with or without antilock brakes. In how many ways can the car be ordered with regard to these options?
3. How many different four-letter radio station call letters can be formed if the first letter must be W or K?
4. A social security number contains nine digits. How many security numbers can be formed? How the Fundamental Counting Principle can be used to solve counting problems?
Examples:
1. The school cafeteria offers a choice of two main courses (grilled cheese sandwiches or soup of the day) and five deserts (jello, pudding, fruit cups, sundaes, or granola bars). How many different lunches could you have?
2. John is color blind. He has 5 different pairs of pants, 8 different shirts, 9 pairs of socks varying in color and 3 pairs of shoes. How many different "outfit" can John show up in school in if he must wear pants, socks, a shirt and shoes? Fundamental Counting Principle
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