Probability can be defined as chances of occurrence of an event. Probability always lie between 0 and 1. Only in the ideal cases, it can be zero or one. If Probability of happening of an event is higher, it assures that chances of occurrence of that event is also high.
Probability of an event X is written as P (X). Complement of an event X is the event (not X) that is in the event of X not occurring.
Probability in this case will be given as P (not X) = 1 – P (X).
Joint probability of two events X and Y can be given as:
P (X ∩ Y).
This type of probability shows that both events X and Y happen simultaneously. This probability is known as Intersection probability. If two events are independent then intersection probability is given as:
P (X and Y) = P (X∩ Y) = P (X) P (Y).
If either X or Y or both occur at same time, then it is known as the Union of the events X and Y and is given mathematically as P (X U Y) and if events X and Y are mutually exclusive then probability of occurrence will be given as:
P (X or Y) = P (X U Y) = P (X) + P (Y).
Law of probability is called addition probability in which probability of X or Y equals to addition of probability of X and probability of Y and minus the probability of X and Y from this addition.
P(X or Y) = P (X) + P (Y) – P (X ∩Y) where P (X ∩ Y) = 0.
If 8 red balls,7 blue balls 6 green balls, find the probabilty of picking one ball that is red or green?
Let P(X) = Probability of drawing the red ball & let P (Y) be Probability of drawing the green ball. Then Total outcomes are 17. So, P (X) = 8 / 17 & P(Y) = 6/17. Therefore P (X or Y) = 8/17 + 6/17 = 14/17.