Anything Math
Post Reply
 
Thread Rating:
  • 0 Votes - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
01-03-2017, 02:21 AM (This post was last modified: 01-03-2017 02:24 AM by Robvalue.)
RE: Anything Math
Hehe okay Big Grin If you draw out a probability tree, starting with the branches "guaranteed rare", "uncommon" and "undefined card", that should help. Then complete the probabilities after that of finding rares (you've already calculated some of this) and see how it all works out. I'll give you the solution if you want, but I didn't want to spoil it in case you wanted to work on it. Obviously the uncommon branch will become redundant, so you needn't continue it.

I'll give you a much simpler example to show you how conditional probability works.

Say we have a group of people:

10% are men with blue eyes
30% are men with brown eyes
50% are women with blue eyes
10% are women with brown eyes

Given that we have selected a man, what's the probability that he has blue eyes?

You can probably see immediately that it's 1/4. The 40% that contain men becomes the whole probability space. So we need to know how much of that space is taken up by men with blue eyes.

10% / 40% = 1/4

In the card example it's more complex, but the principle is the same.

I have a website here which discusses the issues and terminology surrounding religion and atheism. It's hopefully user friendly to all.
Visit this user's website Find all posts by this user
Like Post Quote this message in a reply
07-03-2017, 10:26 PM
RE: Anything Math
(28-02-2017 12:37 AM)Robvalue Wrote:  I have a little challenge I made up Smile Please put solutions in spoilers! Probably quite easy for those well versed in probability.

I buy booster packs for a card game. Each pack contains 10 cards. The cards can be common, uncommon or rare. A pack always contains a guaranteed rare card, and two guaranteed uncommon cards. The remaining 7 cards can each be of any rarity. For each one, 95% of the time it will be a common, 4% of the time an uncommon and 1% a rare.

I open a booster pack, and randomly select a card from it to look at. It's a rare!

What is the probability that there's at least one more rare in the pack?

I'll give the solution to this below, for anyone who is interested.

For any events A and B:

P(A and B) = P(A) * P(B given A)

(When A and B are indepedent, the second term on the right just becomes P(B), which is the familiar way of calculating probabilities.)

P(B given A) = P(A and B) / P(A)

Let A = First card is a rare; B = Second card is a rare

There's two ways I can pick a rare for my first card, either the guaranteed rare, or a lucky pick from one of the 7 undefined cards:

P(A) = 1/10 + 7/10 * 1/100 = 1/10 + 7/1000 = 107/1000

P(A and B) = P(Guaranteed then lucky pick) + P(Lucky pick then second rare)

= 1/10 * ( 1 - [99/100]^7) + 7/10 * 1/100 * 1

(Morondog correctly identified the probability of getting a rare from one of the 7 undefined cards, being one minus the probability of getting no rares. Getting the second rare is guaranteed after getting a lucky pick first, because the guaranteed rare is still there!)

So P(B given A) = [1/10 * ( 1 - [99/100]^7) + 7/1000] / [107/1000]

=0.129 to 3dp

If I put all that into the calculator correctly!

Please let me know if you've spotted a mistake in my calculations.

I have a website here which discusses the issues and terminology surrounding religion and atheism. It's hopefully user friendly to all.
Visit this user's website Find all posts by this user
Like Post Quote this message in a reply
07-03-2017, 10:54 PM
RE: Anything Math
(07-03-2017 10:26 PM)Robvalue Wrote:  
(28-02-2017 12:37 AM)Robvalue Wrote:  I have a little challenge I made up Smile Please put solutions in spoilers! Probably quite easy for those well versed in probability.

I buy booster packs for a card game. Each pack contains 10 cards. The cards can be common, uncommon or rare. A pack always contains a guaranteed rare card, and two guaranteed uncommon cards. The remaining 7 cards can each be of any rarity. For each one, 95% of the time it will be a common, 4% of the time an uncommon and 1% a rare.

I open a booster pack, and randomly select a card from it to look at. It's a rare!

What is the probability that there's at least one more rare in the pack?

I'll give the solution to this below, for anyone who is interested.

For any events A and B:

P(A and B) = P(A) * P(B given A)

(When A and B are indepedent, the second term on the right just becomes P(B), which is the familiar way of calculating probabilities.)

P(B given A) = P(A and B) / P(A)

Let A = First card is a rare; B = Second card is a rare

There's two ways I can pick a rare for my first card, either the guaranteed rare, or a lucky pick from one of the 7 undefined cards:

P(A) = 1/10 + 7/10 * 1/100 = 1/10 + 7/1000 = 107/1000

P(A and B) = P(Guaranteed then lucky pick) + P(Lucky pick then second rare)

= 1/10 * ( 1 - [99/100]^7) + 7/10 * 1/100 * 1

(Morondog correctly identified the probability of getting a rare from one of the 7 undefined cards, being one minus the probability of getting no rares. Getting the second rare is guaranteed after getting a lucky pick first, because the guaranteed rare is still there!)

So P(B given A) = [1/10 * ( 1 - [99/100]^7) + 7/1000] / [107/1000]

=0.129 to 3dp

If I put all that into the calculator correctly!

Please let me know if you've spotted a mistake in my calculations.

Blink

Just when I think I understand probability. Weeping

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
Find all posts by this user
Like Post Quote this message in a reply
[+] 1 user Likes Full Circle's post
25-05-2017, 05:27 PM
RE: Anything Math
(26-02-2017 01:45 PM)morondog Wrote:  
(22-02-2017 12:28 AM)Full Circle Wrote:  The IRR is the interest rate, also called the discount rate, that is required to bring the net present value (NPV) to zero. That is, the interest rate that would result in the present value of the capital investment, or cash outflow, being equal to the value of the total returns over time, or cash inflow.

That's about as clear as a shit sandwich. Jesus. Someone needs to rewrite that.

What do you need to calculate? This IRR thing? The page you linked has instructions for how to get Excel to do it automagically. I vote do that if all you want is the IRR. If you want something in-depth, for what purpose are you calculating it?

That is exactly right...the IRR equals exactly where NPV is 0.

But its not that simple of a concept to someone just learning it. It can take a while to wrap your mind around it.

Wikipedia actually has a good article on the matter. Their formula can help someone visualize how it works better.

https://en.wikipedia.org/wiki/Internal_rate_of_return
Find all posts by this user
Like Post Quote this message in a reply
25-05-2017, 05:31 PM (This post was last modified: 26-05-2017 07:18 AM by swimmyswammysamsonite.)
RE: Anything Math
Full Circle Wrote:
The IRR is the interest rate, also called the discount rate, that is required to bring the net present value (NPV) to zero. That is, the interest rate that would result in the present value of the capital investment, or cash outflow, being equal to the value of the total returns over time, or cash inflow.

Its not a very easy concept to wrap your mind around. But it sure is cool when you finally "get it."
Find all posts by this user
Like Post Quote this message in a reply
26-05-2017, 04:27 AM
RE: Anything Math
(25-05-2017 05:31 PM)swimmyswammysamsonite Wrote:  Full Circle Wrote:
The IRR is the interest rate, also called the discount rate, that is required to bring the net present value (NPV) to zero. That is, the interest rate that would result in the present value of the capital investment, or cash outflow, being equal to the value of the total returns over time, or cash inflow.


That is correct...IRR equals exactly where the NPV equals 0.

Its not a very easy concept to wrap your mind around. But it sure is cool when you finally "get it."
I have nothing to say on topic, just your username is utter gold. Laugh out load Thumbsup

Having problems with your computer? Visit the Free Tech Support thread for help!
Find all posts by this user
Like Post Quote this message in a reply
[+] 1 user Likes OakTree500's post
26-05-2017, 07:03 AM
RE: Anything Math
I've learned all about this now. It's interesting! Here's my attempt to describe it off the top of my head.

The Net Present Value is what the whole project is worth right now, after scaling back expected future income/expenses. It's like doing the opposite of compound interest, to work out what amount of money now would be worth X amount in 10 years. The further things are in the future, the less they are worth now, because of all those years of interest you will have missed out on. If you expect your money in the business to be worth 10% more each year say, then you'd have to divide by 1.1 for each year it is in the future. (You multiply by 1.1 to add 10% for a year, so dividing by the same number would take you in the other direction. Don't make the common mistake of "taking 10% off" to go back, because this isn't the same thing. 90% of 110% is not 100%.)

So the Internal Rate of Return is the rate of interest where, after scaling everything back to the present, you break even. If your money grows at that rate, the whole project would leave you no better or worse off. So it represents a baseline. If your interest rate is above that, then the project is expected to give a positive return. Below it, you expect to lose. Non-financial concerns aside, this means you want your interest rate to be a safe amount over the IRR to consider taking on the project.

I have a website here which discusses the issues and terminology surrounding religion and atheism. It's hopefully user friendly to all.
Visit this user's website Find all posts by this user
Like Post Quote this message in a reply
Post Reply
Forum Jump: