### Standard 11: Probability

In grades 9-12, the mathematics curriculum should include the continued study of probability so that students can:
• Use experimental or theoretical probability, as appropriate, to represent and solve problems involving uncertainty
• Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 6-8, page 229
How probability is estimated depends on what is known about the situation. Estimates can be based on data from similar conditions in the past or on the assumption that all the possibilities are known.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
Estimate probabilities of outcomes in familiar situations, on the basis of history or the number of possible outcomes.

• Use simulations to estimate probabilities
• Benchmarks 11B (Common Themes: Models)
Grades 6-8, page 269
Mathematical models can be displayed on a computer then modified to see what happens.

Benchmarks 9D (The Mathematical World: Uncertainty)
Grades 9-12, page 230
A physical or mathematical model can be used to estimate the probability of real-world events.

• Understand the concept of a random variable
• Create and interpret discrete probability distributions
• Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
Estimate probabilities of outcomes in familiar situations, on the basis of history or the number of possible outcomes.

• Describe, in general terms, the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed:
• Benchmarks 12E (Habits of Mind: Critical-Response Skills)
Grades 9-12, page 300
Wonder how likely it is that some event of interest might have occurred just by chance.

and so that, in addition, college-intending students can:
• Apply the concept of a random variable to generate and interpret probability distributions including binomial, uniform, normal, and chi square