Contitional Probability

Fremen

I have a job interview coming up soon-ish which relies fairly heavily on conditional probability. Thing is, I have little to no experience solving conditional probability problems. I need practice, and fast.

If you know or can think of any interesting ones (and have some time to kill), post 'em up here and I'll do my best to solve them.

Cheers

aequinoctium

1st examples of conditional probability that every learns are to do with card games - usually poker


what is the probability of getting
i)4 kings
ii)royal flush
iii)a diamond and a heart
etc.

when each card is selected separately and not returned to the deck

Colonel Sanders

as spoken about on here before, 2 famous examples are the monty hall problem and the prosecutor's falacy. See wikipedia/google for details!

Fremen

Right, this has been wrecking my head for about twelve hours now.
Assume parents are equally likely to have a boy or a girl.

If there are two siblings at least one of which is a girl, what are the odds both the siblings are girls?

If the eldest is a girl, what are the odds both are girls?

My answer to the first question is 1 in 3, but my answer to the second question is 1 in 2.
The second question only gives the extra information that the girl is older. Why would this change things? (or more likely, why is my second answer wrong?)

EDIT: something to do with cartesian product spaces, maybe? I'm hopelessly confused. Sigh...

Pherekydes

In the first case, the sample space is {GG} {GB} {BG} so the answer is 1/3.

In the second, the sample space is {GG} {GB} so the answer is ½.

The second sample space has no {BG} because the eldest is a girl.

MathsManiac

What's wreckin' my head is trying to figure out how a job interview can "rely heavily on conditional probability".

Is there a test or something first, or did you get told that you're going to be interviewed by a bunch of people who are going to ask you questions about conditional probability? (This strikes me as a slightly bizarre means of recruiting staff and makes me wonder what the job is.) Here's a problem for you:

Consider the following events:
E = the employer is bonkers
F = the employer recruits staff by asking them questions about condidtional probability
G = I want to work for this employer
(i) Find P(E|F)
(ii) Find P(G|E)
(iii) Hence, or otherwise, find P(¬G|F)

The answer to (iii) might solve your problem.;)

Fremen

It's a job in trading, which I need to show numerical ability for, along with a knack for probability. It's not just contitional probability, but probability in general. It's just that I'm not that familiar with the stuff which requires the use of bayes' theorem.

They'll ask a good few probability questions in the interview. I know they like to throw 'curveballs' to try to rattle the interviewee, which is why I'm studying.

I think you've missed something: P(G|E) approaches one as my employability approaches zero.

I have a shrewd suspicion I know who you are. Can you do headstands?

MathsManiac

Well, for introductory stuff on condidtional probabaility, I would recommend one of the supplementary booklets for dealing with the probability option at leaving cert.

Regarding Bayes theorem, check this out:
http://www.ou.edu/ouphil/faculty/chris/bayes2.pdf

(And I can't do headstands!)