Anxious Unpredictable Manipulative Netherless Only

Probability test is just 9hrs away.

I can feel it already.

Arithmetric Progression, Geometric Progression covers the 1st half.

Basic probability, Compound event, and Mutually exclusive probability covers the rest.

Lets make things "complicated" to ease the learning process:

Q1 A bag has 4 boxes, A box has 4 packets, A packet has 4 seals, A seal has 4sweets.
It was said that Each sweet was packaged with a unique number starting arithmetically
from 1 to n.
Find the probability of the sweet obtained is labelled 4.

A: This may seems confusing with so many 4's. Some may suggest to draw diagrams. U will end up 128 branches, by the time u finish the diagram, you realise how stupid u were.

It's simple. convert the relation: 4(4)(4)(4) = 128. which is the total number of sweets, also the number of possible outcome. as stated 1 to n, increasing arithmetically,
It can be concluded the pack contain labels from 1 to 128.
So the probability of getting 4, is nothng difren from the Probability of getting any other number,

P(4) = 1/128

done.


Q2. In A survey of men and women, the probability of a men chosen is not swimmer is 0.2, the probability of the swimmer chosen is a women is 0.4 . The probability of the person chosen swims is 0.7. State the probability of the person chosen is a female.

If you were to draw the Probability Tree out, and sort the value out. I would be Quite Confusing,
You may easily got stucked like a pile of shit. And, It would look like this:


SMen (0.6)

0.7 Swims
SWomen 0.4
Event
S'Men 0.2
0.3 Swims'
S'Women (0.8)

Aiyo, but now they duwan to see from the swimming event, but from the gender. So how?
Die. Use Independent Event formula.P(A) X P(B) then GG.

I always use a method to check in such situation, which Ms. Geetha doesn't encourage, she label it "too complicated". Here's how

Understanding probability as how probable is an event to turn out such outcome.
E.g.
The probability for Anna's marriage to be succesful is 1/10. Means for every 10 marriage, she will Divorce 9 times, and only manage to maintain 1.

Applying teh same concept, Lets use Sampling
Let The total number of person in this survey = X
and X will be 1000.

So now using the same tree,

SMen 0.6 [ 700x0.6]ppl

0.7 Swims ( 700ppl)
SWomen 0.4 [700x 0.4]ppl
1000ppl
S'Men 0.2 [ 300x 0.2]ppl
0.3 Swims'(300ppl)
S'Women 0.8 [300 x 0.8]ppl

With this you will get the weightage of each portion.
Your answer would be the {total number of female / total number of people}

which is { (total female swimmer + total female non swimmer)/ total no. of people}

This is just the understanding of how you get to know probability through sampling.
Indeed the direct way is to add up the total probability involved in this event(women):

0.7x0.4 + 0.3X0.8 = Answer

But you dont memorise formula's, you understand them. ;)