# 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

• Probability of a Jack when card the withdrawn from deck =  4/52,  if it is said
• What is probability to withdraw a Jack of Spade from the deck = 1/5

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

•           P = (no. total x color marbles)/ Total no. of marbles in the bowl

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

• If the marbles are NOT replaced the P=   (no. total x color marbles- 1 )/( Total no. of marbles in the bowl – 1)

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.

•           Probability of independent event  = p1 x p2= Where P1 and P2 are probabilities of 2 events

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

•           Probability of Mutually exclusive event : P1 + P2 and so on  (P1 and P2 is the probability of  each event)

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

•         Probability of non- mutually exclusive event is :  P1 + P2 – ( Proabability of P1,P2 together)

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:

• Find out total number of combination possible this typically found out by cmobination formula : 5C2
• Probability of an head outocme – (1/2) ^ 4
• Probability of  an tail outcome  –  (1/2) ^ 1
• So the total outcome is – 5C2 x (1/2) ^ 4 x (1/2) ^ 1

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