Probability: Addition rule

Today I'm going to share a video uploaded by (KHAN academy) featuring 

Addition rule of Probability 

• If there are two events Say A and B then

P(A or B) = P(A) + P(B) - P (A and B).

how is this derived...??

excited...!!!

Check this video out:

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Probability: picking out ball from bag

Probability can be explained through various examples, out of those in this thread I'm picking up one of those i.e.

Probability: picking out ball from bag

 

    In one of my post I've explained all of the possibilities of outcomes of tossing a coin, or Picking up a card from well shuffled deck of 52 cards.

Now here is the third one picking a ball out from a bag or bucket.

   • Let we have a bag in which we are having 3 red ball, 4 green ball and 5 yellow ball.

Let's check it out different event,

• Probability of ball from bag

     in total we are having 12 balls.

if we are to ask find the probability of 

1. Green ball

• sol.  favourable outcomes will be = 4, as we're having 4 green balls.

     then Probability will be = 4 / 12 or 1/3

2. red ball 

              Probability will be =  3/12 or 1/4

3. Yellow ball 

             Probability will be =  5/ 12

  let's have some more questions

4.  No green ball.

             here we have to think twice for favourable outcomes, no green ball means we can have yellow and red as well so outcomes will be

3 + 5 = 8

      Probability will be =  8/12 or 2/3.

5. Any ball 

    this is a sure event every event is our favourable outcome hence Probability will be =  12/12 or 1.

6. No ball 

     this is impossible event, no ball should picked out means favourable outcomes will be 0,  Probability will be = 0/12 or 0.

     Hence I hope you've​ got this topic. If you want to add here something then let me know via comment.

       For our other Probability based popular topics click below links

• Probability: Tossing a coin

•  Probability: Card System

                                       

Probability: card sysytem

        In one of my previous Tutorial regarding probability I had shared the concept of probability of having coin based problem or picking out a ball from any bag.

Probability: Card System

  Before going down do read this (recommended)

• Probability- based upon coin related problems

further I can say Any event which have two  equally possibilities at most, will result as same as coin based problem does.

• A video by Khan academy (briefing Probability of drawning cards)

       •  Taking that topic to the next level I'm going to share a video (uploaded by KHAN academy)

explaining cards based problems and their various probabilities accordingly.

      •  Out of several videos I have selected this for you to save your time as this video is clearly explained and also oriented for the topic.

      •   Do check this video out and let me know if you're having any doubts I would like to hear from you.

Probability

Hello everyone,
Today's topic is:

PROBABILITY

    This is one of my favourite topic of Mathematics because this is only single formula based Topic in early stage but afterwards in advance level probability may consist some advance topics like (permutation, combination, statistics...)

But in this tutorial I'll be explaining only that single formula i.e.

P(E) = n(f) / n(t)

here,
P(E)  - probability of an event

n(f)  - no of favourable outcome

n(t)  - no of total outcome

event is refer to happening​ the task

outcomes are refer to result which can be favourable or non favourable too,

• this can be understood briefly with following example-

       suppose we have a coin and we have to toss this now the result may vary with head or tail,but the possibility of occurring either head or tail are equally likely i.e. 50-50.

Now toss the same coin twice (or tossing two coins one time) the result may be in the forms
HH, HT, TT, TH
H - head  T- tail

means both head can be resultant or bot tail can be or either head and tail or vice verse, In this situation we are having four outcomes.

If It is ask to find the probability of having head at least one time then favourable outcomes will be
HH, HT, TH

hence P(E)= 3/4

and if it is ask to find the probability of having at most one head then favourable outcomes will be
HT, HH, TH
again P(E)= 3/4.

       One more thing I want to add in this thread is sum of the probabilities of all elementary events are equals to one(1).

  If I pick first situation of having at least one head P(E) = 3/4
and probability of having no heads
outcome will be TT
P(E') = 1/4

then sum of these probabilities of elementary events are

3/4 + 1/4 = 4/4
              = 1

For more explanation watch following video

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