Introduction:

The word ‘Statistics’ has been derived from either Latin word ‘Status’ or Italian word ‘Statista’, which means a political state. The statistics is used for solving or consider the problems of the state he statistics theory is depending on events is either independent or dependent.  If the outcome of one event concerns the outcome of another, then the events are said to be Dependent Events such that P(A / C ) `!=` P(A) and also note that    P(A / C ) = P(A`nn` C) / P(C).

 

 

Events:

Events means any possible outcome or combination of outcomes is called an event. That is every subset of the sample space S is called an event. Events are usually denoted by A, B, C, D, E,F. When a coin is tossed, getting a head or tail is an event. S = { H, T}, A = {H}, B = {T}. Here events A and B are subsets of the sample space S. let us see dependent events statistics.  

Dependent events statistics:

Events are dependent if the outcome of one event concern the outcome of another. For example, if you draw three colored balls from a bag and the first ball is not returned before you draw the second ball then the outcome of the second draw will be pretentious by the outcome of the first draw.

For example A and B are dependent events and then the probability of A happening and the probability of B happening, so given A, is P (A) × P (B after A).

P(A and B) = P(A) × P(B after A)

P(B after A) can also be written as P(B | A)

then P(A and B) = P(A) × P(B | A)                                                                       [Sources :onlinemathlearning]

 

Example:

A purse contains eight $10 balls, five $15 balls and three $20 balls. Two balls are selected without the first selection being replaced. Find P ($10, then $10)

Solution:

There are eight $5 balls.

There are a total of sixteen balls.

P ($10) = 4/ 16

The result of the first draw pretentious the probability of the second draw.

There are seven $10 balls left.

There are a total of fifteen balls left.

P ($10 after $10) = 7/15

P($10, then $10) = P($10) · P($10 after $10) = 4/16 *7/15 =28/240

                                                                                                        =7/60

The probability of drawing a $10 ball and then a $10 ball is 7/60