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10th Grade Mapping
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10th Grade Probability
Understanding real world problems
Understanding real world situations
Problems that students encounter will know relate to real life scenarios - they will no longer be contained to just the classroom. Probability is commonly introduced with gambling. However, it is sometimes started easier, such as picking a marble from a jar.
Problems with context
Contextual problems
Students may not be conducting their own experiments yet. However, probability is the foundation for statistics. The students at this level would be in Level B of the GAISE levels if they were to transition towards statistics.
Area probability
Probabilties based on area
In the spirit of geometry, the probability of a certain event may be calculated using the area of the desired event divided by the entire sample space.
Common scenarios are areas of rectangles, squares, and circles.
Example
Conditional probability
The probability of an event occurring given that another event has already occurred is called a conditional probability.
It is extremely common to create a conditional probability problem from a standard and common probability problem.
Marbles
Exams
Permutations and combinations
Permutation - the action of changing the arrangement, especially the linear order, of a set of items. (order DOES matter)
Combination - a selection of a given number of elements from a larger number without regard to their arrangement. (order DOES NOT matter)
Two events
For probability, two events may be independent or dependent. They can also be done with or without replacement.
Two events
Independence
The important thing to remember about independence of events is that one event does not influence the occurence of the second.
Independence
Dice
Coin and card
With replacement
Dependence
Two events are said to be dependent if one event influences the outcome of the other.
Conditional probability is related to dependence.