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This module allows students to explore concepts related to discrete random variables through the use of a simple playing card experiment. Students will compare empirical data to a theoretical distribution to determine if the experiment fist a discrete distribution. This lab involves the concept of long-term probabilities.

Class Time:


Student learning outcomes:

  • The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a discrete distribution.
  • The student will demonstrate an understanding of long-term probabilities.


  • One full deck of playing cards


The experiment procedure is to pick one card from a deck of shuffled cards.

  1. The theorectical probability of picking a diamond from a deck is: _________
  2. Shuffle a deck of cards.
  3. Pick one card from it.
  4. Record whether it was a diamond or not a diamond.
  5. Put the card back and reshuffle.
  6. Do this a total of 10 times
  7. Record the number of diamonds picked.
  8. Let X = number of diamonds. Theoretically, X ~ B ( _____,_____ )

Organize the data

  1. Record the number of diamonds picked for your class in the chart below. Then calculate the relative frequency.
    x Frequency Relative Frequency
    0 __________ __________
    1 __________ __________
    2 __________ __________
    3 __________ __________
    4 __________ __________
    5 __________ __________
    6 __________ __________
    7 __________ __________
    8 __________ __________
    9 __________ __________
    10 __________ __________
  2. Calculate the following:
    • x =
    • s =
  3. Construct a histogram of the empirical data.
    Blank graph with relative frequency on the vertical axis and number of diamonds on the horizontal axis.

Theoretical distribution

  1. Build the theoretical PDF chart based on the distribution in the Procedure section above.
    x size 12{x} {} P x size 12{P left (x=x right )} {}
  2. Calculate the following:
    • μ = size 12{μ={}} {} ____________
    • σ = size 12{σ={}} {} ____________
  3. Construct a histogram of the theoretical distribution.
    Blank graph with relative frequency on the vertical axis and number of diamonds on the horizontal axis.

Using the data

Calculate the following, rounding to 4 decimal places:

RF = relative frequency

Use the table from the section titled "Theoretical Distribution" here:

  • P ( x = 3 ) =
  • P ( 1 < x < 4 ) =
  • P ( x 8 ) =

Use the data from the section titled "Organize the Data" here:

  • RF ( x = 3 ) =
  • RF ( 1 < x < 4 ) =
  • RF ( x 8 ) =

Discussion questions

For questions 1. and 2., think about the shapes of the two graphs, the probabilities and the relative frequencies, the means, and the standard deviations.

  1. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions. Use complete sentences. (Note: These answersmay vary and still be correct.)
  2. Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions. (Note: These answers may vary and still becorrect.)
  3. Using your answers from the two previous questions, does it appear that the data fit the theoretical distribution? In 1 - 3 complete sentences, explain why or why not.
  4. Suppose that the experiment had been repeated 500 times. Which table (from "Organize the data" and "Theoretical Distributions") would you expect to change (and how would it change)? Why? Why wouldn’t the other table change?

Questions & Answers

what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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a perfect square v²+2v+_
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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or infinite solutions?
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ramon Reply
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Differences Between Laspeyres and Paasche Indices
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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what is nanomaterials​ and their applications of sensors.
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what is nano technology
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what is system testing?
preparation of nanomaterial
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
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what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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Smarajit Reply
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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