Math Assignment Help>> Probability Theory & Concepts

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Theory of Probability & Basic Concepts

Defining Experiment:Experiment is defined as an operation which produces some well defined outcomes.

Random Experiment:Random experiments are those which produce possible outcomes. The exact outcomes can’t be produced in advance.

Examples of Random Experiments

a. Rolling an unbiased dice

b. Tossing a fair coin

c. Picking a ball in certain colors

d. Drawing a card from a pack of cards

Results

a. Throwing a coin may case of results either Head(H) or Tail(T)

b. Dice is a solid cube having six faces which are marked as 1, 2, and 3,4,5,6 respectively. Throwing a dice will case of outcomes one of the number out of these numbers.

c. A pack of cards having 52 cards

1. 13 cards of each suit, Spades, Clubs, Hearts, Diamonds

2. Spades & Clubs: Black Cards

3. Hearts & Diamonds: Red Cards

4. Four honors of each suite, these are kings, aces, queens, jacks. These cards are called face cards.

Sample Space:In performing an experiment may result the set S of all possible outcomes, this set S of possible outcomes is called sample space.

In tossing a coin S= {H, T}

Two coins S = {HH, HT, TH, TT}

Rolling d dice S= {1, 2, 3, 4, 5, 6}

Event: Subset of a sample space

Defining probability of an event

Let S is the sample space and E is an event then

E <= S

P (E) = n (E) / n (S)

Important Results

Some of Basic Terms in Probability Theory

Random Experiments, Sample Space, Event, Simple Event, Compound Event, Mutually Exclusive Event, Independents Event, Exhaustive Event, Conditional Probability, Bayes Theorem, Binomial Trials and Binomial Distribution