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Concept of Probability for competitive exams

Concept of Probability

 Here in this post I have included some basic concept of probability that will be helpful to understand the concept of Probability for answering questions in competitive examination: 

Probability of any event to occur is always given by  n/N and   Not to  occur  is (n-1)/N where n is number of possible occurences and N is total number of occurences. 

for example the probability of a head when a coin is tossed is 1/2. As there can be total of 2 occurences either head or tail. 

Some of the typical questions asked in probability section are about : 

Dice : The probability of any outcome = 1/6, for ex. the probability of 5 in throw of dice is 1/6 

Deck of Card:  A deck of the card has 52 card, If the question is asked what is

Marbles in bowl:   Probability of drawing a x colored marble from a set of the marbles, 

Important Note:   In case of cards and marbles an important concpet of REPLACING the marbles or cards back 

Concept of Independent Events, Mutually Exclusive and cominations of both events 

Independent Event : If the two event do not effect the outcome of each other they are said to independent, for ex. the probability in case of toss with a coin and a throw of the dice. Probability of an outcome of head with number for 4. 

Mutually Exclusive Event : If two events can not happen at a time, for example what is probability that a card drwan from a deck will red or spade. If a card is drawn it can be either red or black, a red card can’t be spade. Or what is probability that a dice outcome will be less than 3, this mean the outcome can be 1 or 2 but both can’t occur together 

NON Mutually Exclusive Event : If the two events can happen at time, for ex. probability of drawing a Red Card or King from a deck are non mutually exclusive event, as there are 2 Red card that are Kings, Heart King and Diamond King 

Combination of Mutually Exclusive and Independent Events:  Many times there is a combination of events for ex. what is proabability of getting 4 heads when coins is tossed 5 times.   Proability of in such cases if found out by: 

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