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#### Description:

In this activity, students experiment with different versions of the Monty Hall problem where the goal is to find a prize hidden behind one of three doors. You start by choosing one door without opening it then one of the other two doors that doesn't have the prize behind it is revealed. Then you are faced with the decision to "stay" with the first door you selected or "switch" to the other remaining door. The student has the option to play the game or run multiple trials at once in order to get a better idea of the overall probability of each strategy. Students can also adjust the number of doors they have to choose from. This activity allows students to explore conditional probability as well as bar graphs and trials. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

#### Subjects:

• Mathematics > General

#### Keywords:

Informal Education,Middle School,NSDL,NSDL_SetSpec_ncs-NSDL-COLLECTION-000-003-112-016,High School,Vocational/Professional Development Education,oai:nsdl.org:2200/20120614151525986T,High School Programming,Mathematics,Middle School Programming

English

#### Access Privileges:

Public - Available to anyone

Creative Commons Attribution Non-Commercial Share Alike

#### Collections:

None
Update Standards?

#### CCSS.Math.Content.HSS-IC.A.2: Common Core State Standards for Mathematics

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

#### CCSS.Math.Content.HSS-IC.B.4: Common Core State Standards for Mathematics

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

#### CCSS.Math.Content.HSS-IC.B.5: Common Core State Standards for Mathematics

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

#### CCSS.Math.Content.HSS-MD.A.1: Common Core State Standards for Mathematics

(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

#### CCSS.Math.Content.HSS-MD.A.2: Common Core State Standards for Mathematics

(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

#### CCSS.Math.Content.HSS-MD.B.6: Common Core State Standards for Mathematics

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

#### CCSS.Math.Content.HSS-MD.B.7: Common Core State Standards for Mathematics

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
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