By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. A bag contains 9 red marbles, 5 blue marbles and 7 green marbles. Need to select one marble at a time without replacement. What is the probability that the first marble is blue, the second is blue or green an the third is red.

That looks like the right answer.

### Probability Urn simulator

These are conditional probabilitiesso. Alternatively, we can use a counting argument. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Probability of picking three marbles in order Ask Question. Asked 5 years, 10 months ago. Active 5 years, 10 months ago. Viewed times. Graham Kemp Jaysun Jaysun 1 1 gold badge 1 1 silver badge 4 4 bronze badges. If the second choice was blue or red, one would have to change the analysis.

### Probability of at least two red marbles?

Active Oldest Votes. Rebecca J. Stones Rebecca J. Stones Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

Post as a guest Name. Email Required, but never shown. The Overflow Blog.A bag contains 4 white, 3 blue, and 5 red marbles.

Watched url bundlesFind the probability of choosing a red marble, then a white marble if the marbles are replaced. Find the probability of choosing 3 blue marbles in a row if the marbles are replaced. Find the probability of choosing a blue marble, then a red marble if the marbles are not replaced. Find the probability of choosing 2 white marbles in a row if the marbles are not replaced. Very good. I agree with all of your answers. You have a good understanding of probability with and without replacement.

I actually thought he was lying but he's not I thought he was trolling good job man. OMG thank you! I wouldn't normally do this but it's getting close to the end of the school year. First Name.

**Probability – Example (Marbles Drawn) Part 1 ( GMAT / GRE / CAT / Bank PO / SSC CGL)**

Find P Red. A bag contains 5 red marbles, 6 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red? The probability that all the marbles are red is? A bag contains 9 red marbles, 8 white marbles, and 6 blue marbles. You draw 4 marbles out at random, without replacement. In a bag of 10 marbles, there are 5 blue marbles, 3 red marbles, and 2 white marbles.

Unlock code for samsung note 8Complete the probability distribution table for drawing 1 marble out of the bag. In a bag there are 2 red marbles 3 white marbles and 5 blue marbles.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.

Bag A contains 6 white marbles and 8 black marbles. Bag B contains 1 white and 8 black marbles. I randomly choose between bag A and B and pick a marble from that bag.

The marble is white. Now, without replacement I randomly choose between two bags again, what's the probability that I will pick a black marble? Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Probability of picking a black marble given a white marble was picked [closed] Ask Question.

Asked 2 days ago. Active 2 days ago. Viewed 23 times. How do I do this intuitively?

Flutter sliversIf there's not intuitive way, how do I do this with Bayes rule? Gnana Gnana 1. New contributor. As iota saysMSE is more suited to this level of question, but you still shouldn't take homework problems there until you are able to show some effort.

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The Overflow How many jobs can be done at home? Featured on Meta. Community and Moderator guidelines for escalating issues via new response…. Feedback on Q2 Community Roadmap.

Related 3. MathOverflow works best with JavaScript enabled.Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Related Topics: More Probability Lessons Probability Games In these lessons, we will learn how to calculate probability without replacement dependent events and how to use a probability tree diagram.

What is Probability without Replacement or Dependent Probability? In some experiments, the sample space may change for the different events. For example, a marble may be taken from a bag with 20 marbles and then a second marble is taken without replacing the first marble. The sample space for the second event is then 19 marbles instead of 20 marbles. This is called probability without replacement or dependent probability. We can use a tree diagram to help us find the probability without replacement.

How to find the Probability without Replacement or Dependent Probability? Step 1: Draw the Probability Tree Diagram and write the probability of each branch. Remember that the objects are not replaced Step 2: Look for all the available paths or branches of a particular outcome. Step 3: Multiply along the branches and add vertically to find the probability of the outcome. Example: A jar consists of 21 sweets.

William picked two sweets at random. Find the probability that: i all three sweets are green? Solution: a Although both sweets were taken together it is similar to picking one sweet and then the second sweet without replacing the first sweet. Check that the probabilities in the last column add up to 1.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.Life is full of random events!

You need to get a "feel" for them to be a smart and successful person.

## Simple probability: yellow marble

Events can be " Independent ", meaning each event is not affected by any other events. But events can also be "dependent" So the next event depends on what happened in the previous event, and is called dependent.

Note: if we replace the marbles in the bag each time, then the chances do not change and the events are independent :. A Tree Diagram : is a wonderful way to picture what is going on, so let's build one for our marbles example.

Now we can answer questions like "What are the chances of drawing 2 blue marbles? We love notation in mathematics! It means we can then use the power of algebra to play around with the ideas. So here is the notation for probability:. So we have to say which one we wantand use the symbol " " to mean "given":.

For the first card the chance of drawing a King is 4 out of 52 there are 4 Kings in a deck of 52 cards :. But after removing a King from the deck the probability of the 2nd card drawn is less likely to be a King only 3 of the 51 cards left are Kings :.

Let's build a tree diagram. First we show the two possible coaches: Sam or Alex:. The probability of getting Sam is 0. When we take the 0.

Laravel csrf tokenWhat is the chance that any of them chose the same number? Following the "No, Yes" path Following the "No, No" path Also notice that when we add all chances together we still get 1 a good check that we haven't made a mistake :.

But here is something interesting It is often easier to work out the "No" case and subtract from 1 for the "Yes" case. This idea is shown in more detail at Shared Birthdays. Hide Ads About Ads.

Master journal listIndependent Events Events can be " Independent ", meaning each event is not affected by any other events. Example: Tossing a coin. Each toss of a coin is a perfect isolated thing. What it did in the past will not affect the current toss. So each toss is an Independent Event. Example: Marbles in a Bag 2 blue and 3 red marbles are in a bag. What are the chances of getting a blue marble? The chance is 2 in 5 But after taking one out the chances change! So the next time: if we got a red marble before, then the chance of a blue marble next is 2 in 4 if we got a blue marble before, then the chance of a blue marble next is 1 in 4.

Replacement Note: if we replace the marbles in the bag each time, then the chances do not change and the events are independent : With Replacement: the events are Independent the chances don't change Without Replacement: the events are Dependent the chances change.If you're seeing this message, it means we're having trouble loading external resources on our website.

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Donate Login Sign up Search for courses, skills, and videos. Math Precalculus Probability and combinatorics Basic probability.

Intro to theoretical probability. Simple probability: yellow marble. Simple probability: non-blue marble. Practice: Simple probability. Next lesson. Current timeTotal duration CCSS Math: 7. Google Classroom Facebook Twitter. Video transcript Find the probability of pulling a yellow marble from a bag with 3 yellow, 2 red, 2 green, and 1 blue-- I'm assuming-- marbles.

## Conditional Probability

So they say the probability-- I'll just say p for probability. The probability of picking a yellow marble. And so this is sometimes the event in question, right over here, is picking the yellow marble. I'll even write down the word "picking. And the way we're going to think about it is how many of the outcomes from this trial, from this picking a marble out of a bag, how many meet our constraints, satisfy this event?

And how many possible outcomes are there? So let me write the possible outcomes right over here, so possible outcomes. And you'll see it's actually a very straightforward idea. But I'll just make sure that we understand all the words that people might say, so the set of all the possible outcomes. Well, there's three yellow marbles. So I could pick that yellow marble, that yellow marble, or that yellow marble, that yellow marble. These are clearly all yellow.

There's two red marbles in the bag. So I could pick that red marble or that red marble. There's two green marbles in the bag. So I could pick that green marble or that green marble. And then there's one blue marble in the bag. There's one blue marble.

So this is all the possible outcomes. And sometimes this is referred to as the sample space, the set of all the possible outcomes.During these challenging times, we guarantee we will work tirelessly to support you. We will continue to give you accurate and timely information throughout the crisis, and we will deliver on our mission — to help everyone in the world learn how to do anything — no matter what.

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We will get through this together. Updated: December 10, References. Calculating the probability of multiple events is a matter of breaking the problem down into separate probabilities and the multiplying the separate likelihoods by one another. Note: The probability of the 5s being rolled are called independent events, because what you roll the first time does not affect what happens the second time. To calculate probability, you will need to divide the number of events, or what you want to calculate, by the number of possible outcomes, or how many total options there are.

For example, if you want to calculate the probability of rolling a 1 on a 6-sided die, you have 1 event, which is rolling a 1, and 6 possible outcomes, which are the 6 sides of the die. So, in this case, you'd divide 1 by 6 to get 0. To turn your answer into a percentage, you'd multiply it by and get To learn how to calculate the probability of multiple events happening in a row, keep reading!

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