Probability of balls chosen from an urn

In summary, the conversation discusses the probability of choosing 2 white balls out of 5 balls chosen at random from an urn containing 3 white and 4 red balls. The balls are replaced after each selection, making the probability of getting a white ball always 3/7. The significance of the balls being replaced is explained as having a 3/7 chance of getting a white ball and 4/7 chance of getting a red ball with each selection. The use of binomial distribution is suggested to calculate the probability of getting 2 white balls and 3 red balls.
  • #1
Gott_ist_tot
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Homework Statement


An urn contains 3 white and 4 red balls. A ball is chosen at random ( in a frequency sense) and replaced. What is the probability of the first 5 balls chosen exactly 2 will be white.


Homework Equations





The Attempt at a Solution



Really I haven't made much progress. I do not understand the significance of the balls being replaced. If they weren't replaced that would make sense to me. But with them being replaced I have no idea. Thanks for any help and advice.
 
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  • #2
Because they are being replaced, the chance of getting a white ball will always be 3/7.

So it's like, what is the probability that if you flip a coin 5 times you will get exactly two heads (only instead of 50/50, then chance of getting heads in 3/7).
 
  • #3
The significance of the balls being replaced just means every time you draw a ball you have a 3/7 chance of it's being white and 4/7 of it's being red. So what are the odds of getting 2 white and 3 red. Binomial distribution. Go for it Nietzsche!
 

What is meant by "Probability of balls chosen from an urn"?

The probability of balls chosen from an urn refers to the likelihood that a specific ball will be chosen randomly from a collection of balls contained in an urn. It is a way to measure the chance of a particular outcome occurring.

How is the probability of balls chosen from an urn calculated?

The probability of balls chosen from an urn can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. For example, if there are 10 red balls and 20 blue balls in an urn, the probability of choosing a red ball would be 10/30 or 1/3.

What factors can affect the probability of balls chosen from an urn?

The probability of balls chosen from an urn can be affected by several factors, such as the number of balls in the urn, the number of desired outcomes, and the method of selection (with or without replacement). It can also be influenced by external factors, such as temperature and humidity, which may affect the weight or texture of the balls.

What is the difference between sampling with and without replacement?

Sampling with replacement means that after a ball is chosen from the urn, it is put back into the urn before the next selection is made. This allows for the same ball to be chosen multiple times. Sampling without replacement means that once a ball is chosen, it is not put back into the urn, reducing the number of balls available for the next selection.

Why is understanding the probability of balls chosen from an urn important?

The concept of probability is used in various fields such as economics, genetics, and statistics. Understanding the probability of balls chosen from an urn allows for more accurate predictions and decision-making in these fields. It also helps in understanding the likelihood of certain outcomes and can be used to determine the fairness of a game or experiment.

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