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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!

So,

### 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.

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,
or,
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! 