Probability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one. Probability helps to predict how likely events are to happen. For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible.
Probability
Probability Questions
What is Probability
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of event to occur, how likely they are to happen, using probability.
Probability can range in between 0 to 1, where 0 probability means the event to be an impossible one and probability 1 indicates the certain event.
Note The probability of all the events in a sample space sums up to 1. 
The Line of Probability
Probability can also be shown on a line. Occurrence of any event lies between impossible and certain ( 0 to 1).
Probability Formula
\(Probability \; of \; event \; to \; happen \; P(E)= Â \frac{Number \; of \; favourable \; outcome}{Total \; Number \; of \; outcomes}\) 
Terms Related To Probability
Some of the important terms are discussed here:
Term 
Definition 
Example 
Sample Space  The set of all the possible outcomes to occur in any trial  1.Tossing a coin, Sample Space (S) = {H,T}
2. Rolling a die, Sample Space (S) = {1,2,3,4,5,6} 
Sample Point  It is one of the possible results  In Deck of Cards:

Experiment or Trial  A series of action where the outcomes are always uncertain.  Tossing of a coin, Selecting a card from a deck of cards, throwing a dice. 
Event  It is a single outcome of an experiment.  Getting a Heads while tossing a coin is an event. 
Outcome  Possible result of a trial/experiment  T(tail) is a possible outcome when a coin is tossed. 
Complementary event  The nonhappening events. The complement of an event A is the event not A (or Aâ€™)  Standard 52card deck,
A = Draw a heart, then Aâ€™ = Donâ€™t draw a heart 
Impossible Event  The event cannot happen  In tossing a coin, impossible to get both head and tail 
Types of Probability
There are two major types of probabilities:
Based on the possible chances of something happen. It is based on the reasoning behind probability.
Based on the basis of the observations of an experiment. It can be calculated based on the number of possible outcomes by the total number of trials
Probability Tree
Probability tree diagram helps to organize and visualize the different possible outcomes. Branches and ends of the tree are two main positions. Probability of each branch is written on the branch, whereas the ends are containing final outcome. Tree diagram used to figure out when to multiply and when to add. You can see below a tree diagram for coin:
Probability Examples
Example 1– Find the probability of rolling a â€˜3 with a die.â€™
Solution– Sample Space = {1,2,3,4,5,6}
Number of favourable event = 1
Total number of outcomes = 6
Thus, Probability = 1/6
Example 2– Draw a random card Â from a pack of cards. What is the probability that the card drawn is a face card ?
Solution– Â A standard deck has 52 cards.
Total number of outcomes = 52
Number of favourable event= 4×3 = 12 (considered Jack, Queen and King only)
Probability = \(\frac{Number\ of\ favourable\ outcome}{Total\ Number\ of\ outcomes}\)
= 12/52
= 3/13 Answer!
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