If one dice is rolled randomly, the set of total possible outcome is{1, 2, 3, 4, 5,6} and the set of all outcomes even number is 2,4,6.
From the above example we design some definitions.
The word PROBABILITY is used to indicate a vague possibility that something might happen. It is also used synonymously with chance
Experiment: The process of rolling dice is known as “experiment”
Random Experiment: The process of rolling dice randomly is known as “Random Experiment”
Rolling an unbiased dice.
Tossing a fair coin.
Drawing a card from a pack of well stuffed card
Picking up a ball of certain color from a bag containing balls of different colors
Sample Space: The set of total possible outcomes in an random experiment is known as Sample Space, denoted by S.
For s dice S= {1, 2, 3, 4, 5, 6}
For coin S= {H, T}
If two coins are tossed, then
S= {HH, HT, TH, TT}
Event: Any Subset of a sample space is called an event, denoted by E.
Probability of any event=n(E)/n(S) i.e.
P (E) = n (E)/n(S)
Where n (E) is total number of required outcomes
n (S) is total number of possible outcomes
P(E) is probability of Events
Probability of the event number=3/6
P (E) =1/2
These probability problems are useful for all competitive exams.
