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A Lesson in Probability - Solve Accurately

Probability comes for like 1 mark or 2 … the good is it is easy … the bad is it comes only for a mark or two!

On requests, I have decided to take the plunge and do a piece on probability – all dice, coins and cards come out and play!


1. What is probability?

Probability is the chance of the happening or non-happening of event; denoted by ‘P’.

2. What are events and sample space?

Sample space is the total number of occurrences that can happen.

Event is the occurrence of ‘something’ which we are concerned with.

For example: Jai and Veeru did that coin toss to gamble away their lives – awesome – but it has got an important lesson of probability too.

One coin – what are the possible out comes? – Two, as there can be a Head or a Tail.

Therefore, our sample space (S) = 2 = total number of possible outcomes (either head or tail).

Say, Veeru wanted Heads – how many heads is possible in one coin? – One. Thus 1 is our Event (E)!

3. How to find Probability

Probability is the chance of the occurrence of an event; [P = E/S]

Thus, with E = 1, and S = 2,

Probability of Veeru going to die = E/S = ½ = 0.5!    [But it was different in the film - I know, I know!]

4. Hold on now! If the chances of Veeru’s death is 0.5; what could be the chance of Jai being the one dying?

Again, ½ =0.5!                            [Think the film makers calculated only this probability!]

5.  The ‘Non – event’.

Every event has its corresponding ‘non-event’; which can be denoted as E'. If the ‘event’ is happening, then non-event will not happen and vice versa.

If Veeru is going to die (E), then Jai won’t (E'); if Jai’s (E) going to die then Veeru (E') won’t!

Thus, P(E) + P(E') = 1

In words, probability of event and probability of a non-event add up to 1.

Therefore, 1- P(E) = P(E'),
                  1- P(E') = P(E).

6. AND ‘n’ OR:

First off – AND is multiplying.
OR is for addition.

If a question is worded like this – ‘if the probability of A hitting the target is 1/3 and B hitting the target is ½, what is the probability of A and B, both, hitting the target if a shot is taken by both.’

which means, P(A) AND P(B) = P(A and B hitting the target); P(A) x P(B)

P(A) x P(B) = 1/6.

Now, if the question was worded - ‘if the probability of A hitting the target is 1/3 and B hitting the target is ½, what is the probability of A or B hitting the target?’

which means, P(A) OR P(B) = P(A or B hitting the target); P(A) + P(B)

P(A) + P(B) = 5/6.

7. Some common sample space(s)!

For Coins

One Coin

Two Coins

Three Coins
Sample Space (S) = 2 2 x 2 = 4 2 x 2 x 2 = 8
and so on…

For Dice One Dice Two Die Three Die
(S) = 6 6 x 6 = 36 6 x 6 x 6 = 216
and so on…

For Cards Cards in one suit (Either Spade, Clubs, Hearts or Diamonds) One Pack of Cards/ Deck = Total number of cards Face Cards (King, Queen, Jack and Ace) of all the fours suits together
(S) 13 13 x 4 = 52 4 x 4 = 16

8. Concept of Odds:

Sometimes probability is viewed in terms of ‘odds for’ or ‘odds against’ an event.

Odds in favour of an event = P(E)/P(E')

Odds against an event,
Odds in favour of the non-event
= P(E')/P(E)               

… fairly simple, right? All you got to do is calculate the P(E) and the P(E'); then use the above formulae, if and only if the word ‘odds’ is in the question! Otherwise we calculate the normal probabilities as asked in the question.

That is all for today folks!

Hope this helps!

Good day!

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  1. sir ICICI bank po k lie minimum qualification graduation mang raha, but main jab apply kar rahi hu to waha post graduation pe mandtory mark bana h..plz ans me kya qualification chahiye???

  2. very good sir..its really helpful


  4. sir second allotment nhi ho raha hai or nayi nayi exam conduct kar raha hai ibps jo clear hai usse toh job de ibps

  5. sirf kamana purpose hai kya ibps ka .jo job nhi de raha hai

  6. last year second allotment was done in sept/oct for IBPS PO2 ... hamein hi itna dukhi kar rahe h yar ... :( :(

  7. i scored 134 in RRB PO from AP and general category what r my chances for final selection? plz reply sir

  8. thanks sir....
    but kuch questions v upload kr dijiye..
    jis typ k questions sbi associate po me aa sakte h....

  9. sir provide download option for all your posts

  10. sir plz ye po3 ki reserve list kab tak aayegi kyuki 3 banks ne to apni reserve list ibps ko bhej di h

  11. Sir, As the notification has come for I.T officer, I am from B.E (CSE), Could you pls guide me to crack this ,Pls tell me the way to get that

  12. Sir, You mentioned that for english Objective English(4 th edition), but 5th edition is also there, which one is better?

  13. Ramandeep Sir!! in sholay, Jai's Event was 1 and S was also 1 , probabilty he had to die..


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