Statistics and probability

Statistics and probability

1. Counting

   • All the Subsets of a Set
     • 15 of those subsets are proper, 1 subset
     • {}—both elements are not in the set {a}—a is in; b is not in the set {b}—a is not in the set; b is in {a,b}—a is in; b is in
     • {} (or Ø), {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}, {a,b,c,d}
   • Number of Elements in a Set
     • There are 2 elevated by 4 = 16 subsets
   • Solve Counting Problems Using the Multiplication Principle
     • "If one event can occur in m ways and a second event can occur in n ways after the first event has occurred, then the two events can occur in m × n ways"
       • https://courses.lumenlearning.com/atd-austincc-mathlibarts/chapter/consider-a-set/
     • If there are 2 appetizer options, 3 entrée options, and 2 dessert, there are a total of 12 possible choices

2. Permutations and Combinations

   • Solve Counting Problems Using Permutations Involving n Distinct Objects
     • Determine how many options there are for the first situation
       • Determine how many options are left for the second situation.
         • Continue until all of the spots are filled.
           • Multiply the numbers together.
     • Permutation is an ordering of n objects
     • Permutation problems can be solved using the Multiplication Principle or the formula for P ( n , r )
   • Solve Counting Problems Using Combinations
     • Combination formula
     • Counting principal
       • Consider choice A with 3 options (A1,A2,A3), and choice B with 2 options (B1,B2). If you had to choose an option from A and then an option from B, the overall total number of options would be 3⋅2=6. The options are A1B1,A1B2,A2B1,A2B2,A3B1,A3B2.
   • Solve Counting Problems Using Permutations Involving n Nondistinct Objects
     • If there are n elements in a set and r 1 are alike, r 2 are alike, r 3 are alike, and so on through r k , the number of permutations can be found by

3. Probability

   • Construct Probability Models
     • Identify every outcome
     • Determine the total number of possible outcomes
     • Compare each outcome to the total number of possible outcomes
   • Compute Probabilities of Equally Likely Outcomes
     • The outcomes in a sample space S are equally likely if each outcome has the same probability of occurring.

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