PROBABILITY

PROBABILITY

------->Choosing<-------

Experiment:

 By performing some operation Some well-defined outcomes are get

Sample space: 

All possible outcomes of experiment

Dice: 

Single Dice Rolled  6   Outcomes(1,2,3,...6)

        Two Dice Rolled    36  Outcomes((1,1),(1,2),...(1,6),

                                                          (2,1)(2,2),(2,3)....(2,6),.....

                                                          (6,1),(6,2),.....(6,6))

Coins:

 Tossing Single coin (Head,Trial)

 Tossing Two coin ((Head,Trial),(Trial,Head),(Trial,Trial),(Head,Head))

Cards:

Total 52 cards

          Type:Spades,Clubs,Hearts,Diamonds Each have 13 cards

           Color:  Black: Spades,Clubs

                     Red: Hearts,Diamonds

           Face cards:Aces,Kings,Queens,Jacks

A bag contains 6 white and 4 black balls.Two balls are drawn at random.Find the probability that they are of the same color.

Choosing of 2 balls from 10 balls both are same color

Choosing: 10C2---2 ball in total 10

Same color: White/black

 6C2 2 in 6 balls OR 4C2 2 in 4 balls

                                        OR-->   +

                                      AND-->   x

So (6C2+4C2)

Formula:

                                    Event / Sample Space

Total out come= Sample space=10C2

Events=Selecting 2 ball that are in same color=(6C2+4C2)

(6C2+4C2)/10C2

((6*5/2*1)+(4*3/2*1))/(10*9/2*1)

((15+6)/45)

(21/45)

(7/15)------Two balls are drawn at random.The probability that they are of the same color.