• Experiment (in probability theory) - a procedure that yields one of a set of possible outcomes
• Sample Space - All Possible Outcomes
  • A mathematical set containing all the possible outcomes of a probability experiment
  • S is often used to denote the sample space
• Successful Outcomes
  • A mathematical set containing all the possible outcomes that meet some criteria for success
  • The criteria for success is determined prior to executing the experiment
  • E is often used to denote the set of successful outcomes
  • E S
• Definition 1
  • If S is a finite sample space (i.e., a finite set of all possible outcomes from an experiment)
  • All outcomes in S are equally likely to occur when the experiment is executed
  • E is a set containing all the successful outcomes, and E S
  • Then the probability function, denoted as p(E) =
  • Note:
    • The function p's domain is the set E, where E S
    • The function p's range is a value r, where r R, and 0 r 1

Examples:

1. What is the probability that a card selected from a regular 52-card deck is a Jack?
   • Determine S = {2C, 3C, ..., KC, AC, 2D, 3D, ..., KD, AD, 2H, 3H, ..., KH, AH, 2S, 3S, ..., KS, AS}
   • Determine E = {JC, JD, JH, JS}
   • Determine p(E) = = 4/52 = 1/13
2. What is the probability that a randomly selected integer from the first positive 200 integers is even?
   • Determine S =
   • Determine E =
   • Determine p(E) =
3. What is the probability that the sum of the numbers that appear on two dice is odd after being rolled?
   • Determine S =
   • Determine E =
   • Determine p(E) =
4. In a lottery, what is the probability that a person picks the correct 6 numbers out of 40?
   • The correct 6 form a set, therefore, the order they appear in the set does not matter.
   • This is a counting problem of the form of a permutation or of the form of a combination, which is it?