Chit-Chat with IB - 2022-08-22

6:13 PM

@CuriousMind feel free to ask as many questions as you like.

@InanimateBeing Thanks for the opportunity.

The coin is flipped twice, so the sample space:
$$\{HH,TT,HT,TH\}$$
This means that the sample space $(S)$ of the balls in the bag is:
$$S=\{RR,BB,RB,BR\}$$
***Note:*** $P(E_{RR})=P(E_{BB})=P(E_{RB})=P(E_{BR})=\frac14$<p>

For ease, let's denote the event of drawing a red ball by $X$ and that of drawing a blue ball by $Y$.<br>
I'll be using the [**Bayes' Theorem**](https://en.wikipedia.org/wiki/Bayes%27_theorem) to compute the probabilities ahead.

We know, $P(X|E_{RR})=1 \text{ and } P(Y|E_{RR})=0$<br>

I haven't learned Bayes Theorem yet but it looks intutive.

InanimateBeing

Oh you hadn't done the Bayes' theorem, didn't know that.

Basically bayes theorem is your general probability formula that looks a bit fancy so that it suits the conditional probabilities.

Are you aware of the conditional probabilities?

Curious Mind

I used only intution. So my intution says when you replace the red ball the sample space is RR RB and BR and from this I think the answer becomes 1/3(0+0.5+0.5) for getting blue marble which gives 1/3.

@InanimateBeing Yes after watching few youtube videos.

InanimateBeing

@CuriousMind I didn't get how you are getting 1/3?

Oh wait, I get it, just read your previous comment on the answer post

Curious Mind

@InanimateBeing First you pick Red then we put it back that means we still have {RR,RB,BR}. And getting blue from this sample space is 1/3*0+1/3*0.5+1/3*0.5 .

If we use same logic from case 2 from your last Addendum.

InanimateBeing

6:28 PM

@CuriousMind see, since we know that the 1st marble was red that's why we now know that only {RR,RB,BR} are the possibilities. This does not change the fact that the chance of any of them happening changes their probabilities from 1/4 to 1/3

It is still 1/4.

But if our question had asked only to calculate the probability that the 1st marble is red and the second one is blue then we would have proceeded as you are trying to proceed. But we are asked to calculate the probability GIVEN that the first ball is red.

By mentioning that "GIVEN the first ball is red" that means that now are sample space has changed. It isn't {RR,BB,RB,BR} as it used to be, now it's {RR,RB,BR}.

Curious Mind

Ok I will try to digest this.

InanimateBeing

(Thumbs up)

Curious Mind

6:43 PM

@InanimateBeing OK I see the point now. I am sure I can understand this. Thank you very much for the help :)

InanimateBeing

@CuriousMind great! I'm glad I could be helpful. :-)

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