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Introduction to Probability: Single Coin Flips | Understanding Probabilistic Events | Coin Flip Experiment

Explore the basics of probability with a single coin flip, understanding events, outcomes, and calculations. Learn about permutations, combinations, and the importance of order in probability theory.

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Introduction to Probability: Single Coin Flips | Understanding Probabilistic Events | Coin Flip Experiment

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  1. Lesson #8 Introduction to Probability

  2. Flip a single coin: S = { T , H } Or, if we let X = # heads, S = { 0 , 1 }

  3. P = P(Event) = P(A) = 0  m  n 0  p  1 

  4. REMEMBER! 0  p  1

  5. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  6. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  7. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  8. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  9. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  10. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  11. S= { TT , TH , HT , HH } S= { 0 , 1 , 2 }

  12. nCr or n! = n(n - 1)(n - 2) … 1 Choose r objects from n, without replacement Combinations - order irrelevant Permutations - order is important nPr

  13. 4C2= = 6 AB BA AC CA AD DA BC CB BD DB CD DC 4P2= 12

  14. In general, nPr = n(n-1)(n-2) … (n-r+1) (n-r)(n-r-1) … (1) (n-r)(n-r-1) … (1)

  15. In general, nPr = n(n-1)(n-2) … (n-r-1) (n-r)(n-r-1) … (1) (n-r)(n-r-1) … (1)

  16. For any combination (subset) ofrobjects, there arer!arrangements or permutations.

  17. (47!) (5)(4)(3)(2)(1) (47!) 249,900 = .0962 P(Ace of hearts) =

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