Probability of balls chosen from an urn

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SUMMARY

The probability of drawing exactly 2 white balls from an urn containing 3 white and 4 red balls, with replacement, can be calculated using the binomial distribution. The probability of drawing a white ball remains constant at 3/7 for each draw due to replacement. The scenario is analogous to flipping a biased coin 5 times, where the probability of heads represents drawing a white ball. The solution requires applying the binomial probability formula to find the odds of obtaining 2 white and 3 red balls in 5 draws.

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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.


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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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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).
 
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!
 

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