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October 8, 2022About this post
Probability undoubtedly is a vast topic with applications in various fields. With countless applications in research, sports, games, weather forecast, insurance, business analytics, etc, probability is one of the most important topics that we must be aware of.
The aim of this topic is to help you build your basics in Probability. In the section introduction to Probability we have shared some important terminologies involved in Probability problems. The exercises contain solved question and answers. The key to solving a problem is knowing how to approach the problem. When solving exercises, we recommend you to try solving the problems on your own, then view the solutions. That way we believe you can strengthen your approach in solving problems on Probability.
Introduction to Probability
Experiment :
An experiment is a trial that gives well defined set of possible outcomes.
Outcome :
It is the result of single trial of an experiment.
Event :
Event is one or more outcomes of an experiment.
Random Experiment :
An experiment whose outcome cannot be predicted in advance with certainty.
Example : Tossing a coin is a random experiment whose outcome is either heads or tails.
Sample Space(S) :
Set of all possible outcomes of an experiment.
Example : Sample space of a rolling a dice - {1, 2, 3, 4, 5, 6}
Event :
It is the subset of a sample space.
Probability :
Probability is the measure of likelihood that an event will occur.
Probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes.
i.e, Probability of event A = $\frac{\text{Number of ways event A can occur}}{\text{Total number of possible outcomes}} $
P(A) = $\frac{n(A)}{n(S)}$
where,
P(A) is the probability of event A
n(A) is number of ways event can occur,
n(S) is the total number of possible outcomes
About Playing Cards
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣.
Cards of Spades and clubs are black cards.
Cards of hearts and diamonds are red cards.
The card in each suit, are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2.
King, Queen and Jack (or Knaves) are face cards. So, there are 12 face cards in the deck of 52 playing cards.
