math people: need help calculating chance

[Yuri-G]

I'm trying to figure some stuff out and I need to know how to calculate the chance of something occuring, when given multiple opportunities for that particular event to occur.

The scenario I'm looking at is one where, with each chance for the event to occur, it grows more likely until it is 100% once you've exhausted all chances.

For example, if you had four red marbles in a pile of 60 marbles, and you drew one marble, the chance of it being red is 1/15. Assuming you remove the marbles every time you pick one out and don't put them back in, the chance of pulling at least one red marble after 57 tries is 100%. But how do I figure out the probabilities in-between? And how do I figure out the chance of pulling two red marbles after 2 tries, or 2 red marbles after 57 tries, for example? There has to be a formula for this, but I've no idea what it is. The fact that you're removing the marbles, which increases the chance every time, is what's tripping me up and making this harder than it should be.

I am at a loss here and google has, for the first time in my life, completely failed me. Help me, math people. You're my only hope.

Note that this is not for school and you are not helping me cheat on anything. I could you what it's really for but it would make me sound really nerdy.

[Viena]

Binomial distribution - Wikipedia, the free encyclopedia

Edit: And a more practical answer would be to use Excel with the following expression:

=BINOMDIST(2;57;1/15;FALSE)

2 - You want to calculate the chance of getting 2 red balls out of a number of tries
57 - That's the number of trials
1/15 - Chance of success on each trial
FALSE - Not cumulative, it means that you are calculating the chance of getting exactly 2 successes, TRUE is cumulative, and would mean calculating the probability of getting at most 2 successes.

The result is: 0.159541284 (~16%)

[Yuri-G]

Thanks. Although that wiki page is pretty intimidating. I guess that 5 on the AP Calc test doesn't mean I'm good at math for the rest of my life, after all

I'll have to study up on this stuff sometime, it's apparently more complicated than I gave it credit for.

[0ni0n]

The chance of getting a red marble first try is 4/60.

Assuming you did get a red marble first try, the chance of getting another one is then 3/59.

The chance of getting two red marbles in the first two tries is 4/60 x 3/59 = 0.00339.

[Demosthenes11]

no offense, but people suck at math if they cant get a 5 on calc ab ap test lol

stats is a whole new monster compared to calc too.

[Correction]

no offense, but people suck at math if they cant get a 5 on calc ab ap test lol

stats is a whole new monster compared to calc too.

Calc BC was no picnic either. I hated that and stats the most.

[0ni0n]

or 2 red marbles after 57 tries?

Well, we already know it's 100% chance that we will get at least 1 red marble out of 57 tries, so the question literally translates into calculating the probability of getting 1 red marble in 56 tries, which will be (1- the probability of getting 56 blue marbles out of 59 marbles in 56 tries). The calculation is glaringly tedious.

[Demosthenes11]

Calc BC was no picnic either. I hated that and stats the most.

i'd say bc is retarded easy as well but the concepts are a bit harder...I really am not a good measure because I was the student of the national teacher of the year so >.>