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 :
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Probability of a Jack when card the withdrawn from deck = 4/52, if it is said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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