Find Probability Using an Organized List
Find Probability Using an Organized List is a Grade 7 math skill from enVision, Mathematics, Grade 7, covering Probability. To find the probability of a compound event using an organized list, first list all possible outcomes in the sample space. Then, count the number of favorable outcomes and the total number of outcomes. Explanation An organized list helps you visualize the entire sample space for a compound event. By systematically writing down every possible combination of outcomes, you can ensure no possibilities are missed.
Key Concepts
Property To find the probability of a compound event using an organized list, first list all possible outcomes in the sample space. Then, count the number of favorable outcomes and the total number of outcomes. The probability is the ratio of these two counts. $$P(\text{event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}$$.
Examples Suppose you toss a coin and roll a six sided die. The organized list of outcomes is: (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6). The probability of getting tails and an even number is $P(\text{Tails and Even}) = \frac{3}{12} = \frac{1}{4}$. A bag has one red (R) and one blue (B) marble. A second bag has one green (G), one yellow (Y), and one orange (O) marble. The organized list for picking one marble from each bag is: (R,G), (R,Y), (R,O), (B,G), (B,Y), (B,O). The probability of picking a blue marble and an orange marble is $P(\text{B and O}) = \frac{1}{6}$.
Explanation An organized list helps you visualize the entire sample space for a compound event. By systematically writing down every possible combination of outcomes, you can ensure no possibilities are missed. Once the list is complete, you can directly count the total number of outcomes and the specific outcomes that match the event you are interested in. This method provides a clear and straightforward way to calculate the probability by forming a fraction with these counts.
Common Questions
What is find probability using an organized list?
To find the probability of a compound event using an organized list, first list all possible outcomes in the sample space.. Then, count the number of favorable outcomes and the total number of outcomes.. The probability is the ratio of these two counts.
How do you use find probability using an organized list in Grade 7?
Explanation An organized list helps you visualize the entire sample space for a compound event.. By systematically writing down every possible combination of outcomes, you can ensure no possibilities are missed.. Once the list is complete, you can directly count the total number of outcomes and the specific outcomes that match the event you are interested in.
What is an example of find probability using an organized list?
Examples Suppose you toss a coin and roll a six-sided die.. The organized list of outcomes is: (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6).. The probability of getting tails and an even number is .
Why do Grade 7 students learn find probability using an organized list?
Mastering find probability using an organized list helps students build mathematical reasoning. By systematically writing down every possible combination of outcomes, you can ensure no possibilities are missed.. Once the list is complete, you can directly count the total number of outcomes and the specific outcomes that match the event you are interested in.
What are common mistakes when working with find probability using an organized list?
A common mistake is overlooking key conditions. The probability is the ratio of these two counts.
Where is find probability using an organized list taught in enVision, Mathematics, Grade 7?
enVision, Mathematics, Grade 7 introduces find probability using an organized list in Probability. This skill appears in Grade 7 and connects to related topics in the same chapter.