Probabilities in Statistics can be defined as the possibility of occurrence of any event. Now let us look at statistics Probability in details:
In case of tossing coin, there is a possibility of getting either head or tail on tossing. It means that there are two possibilities. The possibility of getting a head is ½ and the possibility of getting a tail is also ½.
We also observe that the sum of all possible outcomes of any experiment is always 1.Here ½ + ½ = 1
Probability can be calculated as = number of favorable outcomes / total number of possible outcomes.
Let us consider another example of rolling a dice. The possible outcomes of rolling a dice are 1, 2, 3, 4, 5, 6. So total number of outcomes are 6. If we look at the probability of following events:
Probability (Getting a even number). We see that we have 2, 4, 6 as the even Numbers.
So, P (Even Number) = 3/6
Similarly P (Odd Number) = 3/6
P (getting a number less than 5) = It includes all the numbers less than 5, i.e. 1, 2, 3, 4. (The possible outcomes are 4)
So P (getting a number less than 5) = 4 / 6 = 2/ 3
Probability statistics includes the study of different types of probability. We see that the value of probability varies between 0 and 1 (inclusive of both sides). We can divide the events in different classes based on the probability.
Impossible Event: Any event is called impossible if we find that its probability statistics is Zero (0). Let us consider an example of picking a card from a pack of 52 cards excluding jokers. Now what is the probability of getting a Joker.
We know that joker does not exist in the pack of cards, so the probability of getting the joker is zero, so we write-
P (Joker) = 0 / 52. Such an event is called an Impossible Event.
Other example of impossible event is getting number 7 on rolling a dice.
Sure event: A statistical probability of getting the value 1 is called Sure Event. Let us consider any event of throwing a dice.
What is the possibility of getting a natural number less than equal to 6. On every throw, the number we get will be less than or equal to six, so the probability is 1. Such events are called sure events or certain event.
Low probability and high probability events: The events which have the probability near to zero are called low probability statistics and the events which have the probability inclined towards 1 are called high probability events.
If the probability of any event is not affected by the previous events, then such events are called Independent Events, on other hand, if probability of any event is affected by the previous events are called dependent events. Tossing of a coin is an independent event and taking out two cards, one after another is called dependent event, as when we take out the second card after the first card is taken out from the pack, that time there are only 51 cards in the pack.
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.