# Chances Are

## Chances Are by Dolores Lucio-Gomez

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### TEKS

(11)  Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:

(A)  find the probabilities of dependent and independent events;

(B)  use theoretical probabilities and experimental results to make predictions and decisions; and

(C)  select and use different models to simulate an event.

(12)  Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:

(A)  use variability (range, including interquartile range (IQR)) and select the appropriate measure of central tendency to describe a set of data and justify the choice for a particular situation;

(B)  draw conclusions and make predictions by analyzing trends in scatterplots; and

(C)  select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.

(13)  Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to:

(A)  evaluate methods of sampling to determine validity of an inference made from a set of data; and

(B)  recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

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Timeline: 2-3 days

Instructional Focus: Probability – Independent and Dependent Events

Hook:

Based off of “The Lazy Song” by Bruno Mars.

Driving Question(s):

How do you determine if the probability of two events is independent or dependent?

• Students will research the following: independent events, dependent events, replacement, non-replacement. Formulas utilized for independent and dependent events.
• Students will write their findings of independent events involving a coin, a dice, and a deck of cards.  They will also write their finding of dependent events involving two coins, two dice, and a deck of cards.
• Students will compute independent events of the following problem: A jar of marbles contains 4 blue, 5 red, 1 green, and 2 black marbles.  A marble is chosen at random from the jar.  After replacing it, a second marble is chosen.  Find the probability of each of the following: P(green and red), P(blue and black).
• Students will create their own problem with solutions  for dependent events and present to the class in the format they select.

Learning Outcomes/Problem Requirements:

Students will know the vocabulary involved with probability, the formulas to compute probability and identify the difference between independent and dependent events.

Assessments:

• Word Problems on probability – three different levels (basic, intermediate, and advanced).
• More practice on probability.
• Presentation of dependent problem the groups themselves created.

Resources:  Internet Search Engines

Teacher Notes:

• Rubrics –teacher created can be utilized.
• Personally, I have the students create the rubric, I suggest the items we’d like to grade- information, did they solve the problem, research, creativity, etc.  They are to decide the point system and categories they wish to grade each other on.
• I and the students grade each group with the agreed upon rubric they created.
• During the research phase and putting their items to be completed for presentation is graded on a check list of the soft skills we grade the students on.