Introduction to Probability

 

Definition

Probability is defined for a specific outcome in a situation where several different outcomes are possible. If the possible outcomes are denoted A, B, C, D, etc., then the probability of A is defined as:

Examples

Tossing Coins: When you toss a balanced coin, the outcome is either heads or tails. Thus, there are a total of 2 possible outcomes. The probability of tossing a head is

p(Head) = 1/2 = .5 = 50%

Selecting Cards: There are 52 cards in an ordinary deck of cards. Thus, there are a total of 52 possible outcomes.

• The probability of drawing a Heart (there are 13 hearts) is:
  p(Heart) = 13/52 = 1/4 = .25 = 25%
• The probability of drawing an Ace (there are 4 aces) is:
  p(Ace) = 4/52 = 1/13 = .0769 = 7.69%
• The probability of drawing a Green card (there are 0 green cards) is:
  p(Green) = 0/52 = .00 = 0%
• The probability of drawing a card (there are 52 cards) is:
  p(Card) = 52/52 = 1.00 = 100%

Definition

Random Sampling: An independent random sample must satisfy two requirements:

1. Each individual in the population must have an equal chance of being selected.
2. If more than one individual is selected for the sample, there must be constant probability for each and every selection. (Sample with replacement)