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# Simple probability: yellow marble

In order to find the probability of picking a yellow marble from a bag, we have to first determine the number of possible outcomes, and then how many of them meet our constraints. Created by Sal Khan and Monterey Institute for Technology and Education.

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• • • There are several applications of probability:

1) Making decisions that improve one's chances of winning a game that involves both strategy and luck;

2) Determining whether or not playing a gambling game will win or lose money in the long run;

3) For an insurance company, making decisions on monthly premiums, deductibles, and percentages;

4) For a stockmarket expert, pricing options on stocks;

5) For a meteorologist, making predictions about the weather; and

6) In statistics and research, determining if there's likely to be a difference (for example, determining whether a treatment is likely to be effective) based on data collected, or if the data obtained instead just occurred by chance.
• I had this question on a test and couldn't figure out the answer. Maybe one of you can help me. There are marbles in a box. Two-thirds of them are white, half of them are red, and 6 of them are green. How many marbles are in the box and what is the probability of selecting a white marble? • • I understand this but I need help with this question from DeltaMath "In a popular online role playing game, players can create detailed designs for their characters "costumes" or appearance. Shaniece set up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and number of costumes purchased in a single day is listed below.
97 visitors purchased no costumes
26 visitors purchased exactly one costumes
13 visitors purchased more then one costume
Based on these results, express the probability that the next person will purchase more then one costumes as a percent to the nearest whole number " • • What if you want to know the probability of getting a yellow marble if you picked two marbles?
(1 vote) • Let's try to work this out. There are 8 marbles total, 3 of which are yellow. First you pick 1 marble, which has a chance of 3/8 to be yellow. If it's a yellow, great, you're done. But if it's not yellow, you get another chance. There are now 7 marbles left, and still 3 of them are yellow. So now the chance of getting a yellow on the second try is 3/7.
Hmm so what would be the combined chance of both of those events - taking into account that the second event only needs to take place if the first event was a "negative" - i.e. the marble was not yellow. That's kinda hard to think about.

It turns out my last sentence holds a clue to the solution: the second event only happens if the first was a negative. So what if we try to invert the problem: if you pick 2 marbles, what's the probability of not getting at least 1 yellow? That's easier: the first time it's 5/8, the second time it's 4/7, and the combination is just both those events happening. No need for "the second event only if the first didn't happen" or complicated things like that. The new question is simply: what is the chance of getting no yellows in 2 tries?

I'll leave the details of the calculation to you - the result is 20/56 = 5/14.

So what does this tell us? The chance of not getting a yellow after 2 tries is 5/14. But we wanted to know the inverse of that: the chance of getting at least 1 yellow. We get that by subtracting 5/14 from 1. After all, either we get a yellow or we don't: the sum of those two options must equal 100% = 1.

So the probability of getting at least 1 yellow is:
1 - 5/14 = 9/14 or about 64%.
• • The term "space" is often used to describe the set of choices you have when selecting inputs, or the set of solutions you have when describing outputs. In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

You may also hear the term "solution space" which describes the set of possible solutions to a problem. Sometimes, depending on the nature of the problem, especially ones whose solutions are ordered pairs or triples, the solutions actually form a line, or area or volume in three dimensional space - so the solution space is some subset of 3-space.

Recall your old friend y = mx + b - given an m and b, the solution space (in this case a line) is the line formed by all (x, y) that satisfy the equation.
• • Let's say you have a bag of marbles and you have 1 yellow marble and 2 purple marbles in the bag.
Then, you decide to draw one marble out of the bag.

But, the problem is, you can't see in the bag, so you want to know how often you will draw the yellow marble.

Thinking about it, you know that there are 3 total possibilities.
Marble 1 (Yellow)
Marble 2 (Purple)
Marble 3 (Purple)

So, there are 3 possibilities, and 1 of them match our criteria.
We can set up a fraction that depicts our situation;
1 (possibility) / 3 (possible outcomes)
That ^ is the way that we right fractions to find out percentages.
Then we can convert that to decimal form which gives us 0.33, which we can then convert it to a percentage which gives us that we have a 33% chance of getting a yellow marble.

Hope this helps,
- Convenient Colleague 