A recent thread on the TINspire Google Group asked about uses of CAS in probability. There are so many possibilities–one uses CAS for binomial probabilities. For example, what’s the probability of getting exactly 3 heads in 5 tosses of a fair coin? A CAS approach expands . The coefficients of h (heads) and t (tails) are the respective probabilities of each outcome and the exponent is the number of trials. Obviously, there’s lots to unpack here to prevent this from being a black box tool, but note the power of the output. The three heads event is represented by the term, and the coefficient is the desired probability, . Early in my career, I taught this by expanding , picking the appropriate term, and substituting for each variable its probability. The great power of this approach is that the meaning of each fractional term remains by the presence of the variables while you gain the answers simultaneously. Also note that while the problem asked only for the probability of exactly 3 heads, the CAS output gives the result of every possibility in the entire sample space. Variations 1) What is the probability of 3 heads in five tosses if the coin was bent in a way that ? Adjust the coefficients to get 0.2304. 2) The technique is not restricted binomial probabilities. If there are three possible outcomes (a, b, and c) where , , and , then what is the probability of exactly 2 as in 3 trials? Because only 2 outcomes are specified for the 3 trials, the third could be either b or c. These two outcomes are highlighted above, giving a total probability of 0.288. While these values certainly could be computed without a CAS, the point here is to use technology for computations, freeing users to think.
Author
Search this site
Twitter Updates
 @vivekanandman16 https://t.co/xTa3Pc7d06 1 month ago
 @vivekanandman16 Oops... copying error in first term of generalization step. Here’s the corrected version: https://t.co/OCHa3DscvM 1 month ago
 @vivekanandman16 Here’s a generalization of the pattern for all powers of the numerator terms. https://t.co/MYVsXjct6N 1 month ago
 @vivekanandman16 My approach is similar to others: https://t.co/VfIoo7dy1K 1 month ago
 @KangarooPhysics @jamestanton Nice...a “wobbly” Sierpinski ! 5 months ago

Recent Posts
Tag Cloud
"four 4s" absolute value algebra AP apps AP Statistics area arithmetic binomial calculus CAS CCSSM conditional probability conics creativity derivative Desmos elementary exploration exponential factoring fingers FiveThirtyEight Five_Triangles fractions geogebra geometry graphing humor identities innumeracy ipad Jo Boaler limits linear lines logarithm lottery marilyn vos savant matrices multiplication normal distribution Nspire number bases parametric pedagogy polar polar functions polynomial precalculus probability problemsolving product rule proof pythagorean Pythagorean Theorem quadratic quadrilateral ratios rule of four sequence series similarity slider square statistics system system of equations tangent lines technology TI Nspire transformation transformations triangle trigonometryCASmusings posts
 September 2018
 August 2018
 July 2018
 March 2018
 January 2018
 August 2017
 July 2017
 June 2017
 March 2017
 November 2016
 August 2016
 July 2016
 June 2016
 May 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 September 2015
 August 2015
 July 2015
 June 2015
 March 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 May 2014
 March 2014
 February 2014
 January 2014
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
 March 2012
 February 2012
 December 2011
 November 2011
 October 2011
 September 2011
 August 2011
 July 2011
 March 2011
Meta
Pingback: Binomial Probability and CAS  CAS Musings