Probability means the chances of happening or occurring of an event
Event:-
Event is the single result of an experiment
Ex. Getting a head is an event related to tossing of a coin
Types of event:-
Various types of events are as follow:
Ex. A professor chooses a student at random from a class of 20 boys. What is the probability that the student chosen is boy?
Favourable cases = 20
total cases = 20
∴ Probability =20/20 = 1
Two events are called dependent if outcome or occurrence of the 1st affects the outcome or occurrence of the 2nd, so that probability is changed.
Ex. A card is chosen at random from a deck of 52 playing cards. without replacing it, a 2nd card is chosen. What is probability that 1st card chosen is king and the 2nd chosen is jack?
Independent Events:-
Two events A and B are called independents if occurring or non-occurring of A does not affect the occurring or non-occurring of B.
Ex. A coin is tossed and a 6 sided dice is rolled find probability of getting a tail of coin and getting ‘2’ on dice?
Probability (Tail) =1/2
Probability of getting ‘2’ of dice =1/6
Some rule of Probability
P (A or B) = P(A) + P(B)
and P(A ∪ B) = P(A) + P(B)
if A and B are independent event
P(A ∩ B) = P(A). P(B)
Ex. From a pack of 52 cards, a card is chosen at random, find the probability that it is either a king or a jack?
⇒ Different types of question asked on probability:-
In these type, questions are based on tossing of coins and obtaining a particular face (Head/Tail) or obtaining same face on two or more coins.
Ex. A coin is tossed twice, then find probability that a tail is obtained atleast once?
When coin is tossed twice, total possible outcome = 4
Ways in which tail is obtained = 3
∴ Required probability =3/4
These type of question is based on rolling of one or more dice and getting a particular number on the face or a sum of faces of dice.
Ex. A single dice is a rolled what is the probability of getting a 2 or 6?
These types of questions are based on choosing a ball of a particular colour from one or more bag containing different coloured balls.
Ex. In a bag, there are 3 white, 4 red and 5 Green balls. if two ball are chosen, find the probability of both balls being red ?
Here White balls= 3
Red balls = 4
Green balls = 5
