Understanding of Probability

• Probability is a field of mathematics that deals with chance.
• An experiment is an activity in which the results cannot be predicted with certainty. Each repetition of an experiment is called a trial.
• An outcome is a result of an experiment. An event is any collection of outcomes, and a simple event is an event with only one possible outcome.
• The sample space for a given experiment is a set S that contains all possible outcomes of the experiment. In any experiment for which the sample space is S, the probability of an event occuring is given by the formula P(event) = n(event) / n(sample space).
• The sample space for the experiment in throwing a die is the set of all possible outcomes.
• In the experiment of tossing two coins simultaneously, there are four possible outcomes (HH, HT, TH, TT), so the sample space is {HH, HT, TH, TT}.
• What would be the probability of picking a black card at random from a standard deck of 52 cards?

  • P(black) = n(black) / n(sample space)
  • There are 26 black cards and 26 red cards with a total 52 cards
  • n(black) = 26
  • n(sample space) = 52
  • P(black) = 26/52 is 1/2 or 0.5
• There are 26 black cards and 26 red cards in a standard deck of 52 cards. Within that, there are 13 clubs, 13 diamonds, 13 hearts, and 13 spades.
• In a standard deck of 52 cards, there are 4 Jack face cards, 4 Queen face cards, and 4 King face cards, with a total of 12 face cards.
• What is the probability of rolling, on a fair dice:

  • a 3?
  • Answer:
  • 1/6 because there is only 1 three in a dice while there are 6 faces in total.
• What is the probability of rolling on a fair dice:

  • an even number?
  • Answer:
  • There are 3 even numbers in the 6 face of the dice, namely: 2, 4, and 6.
  • A dice has 6 sides, therefore there are 6 sample spaces.
  • P(even) = 3/6 is 1/2 or 0.5
• What is the probability of rolling, on a fair dice:

  • zero?
  • Answer:
  • P(zero) = n(zero) / n(sample space)
  • There is no 0 in a die. On the other hand, there are 6 sides or sample spaces in a die.
  • P(zero) = 0/6 or 0 (which is impossible)
• What is the probability of rolling, on a fair dice:

  • a number greater than 4?
  • Answer:
  • P(greater than 4) = n(greater than 4) / n(sample space)
  • There are TWO numbers greater than 4, namely: 5 and 6.
  • P(greater than 4) = 2/6 or 1/3
• What is the probability of rolling, on a fair dice:

  • a number lying between 0 and 7?
  • Answer:
  • What are the numbers lying between 0 and 7? Those numbers are 1, 2, 3, 4, 5, 6, which are in the sense, the 6 sides of the dice itself.
  • P(between 0 and 7) = n(between 0 and 7) / n(sample space)
  • P (between 0 and 7) = 6/6 or 1 (which is certain)