An urn contains 9 balls numbered 1 to 9. A ball is drawn with replacement an indefini

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kuusora310

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Hi! I really don't know how to get the answer to this question:

An urn contains 9 balls numbered 1 to 9. A ball is drawn with replacement an indefinite number of times. The number appearing on each draw is noted down in a sequence. What is the length of the shortest sequence such that the probability of getting at least one 5 is at least 80%?

Can someone help me I'm desperate :?:?:?
 
Hey, this is an interesting problem. What makes it hard is the fact that there has to be at least 1 draw of 5. This means that, for example, if I make 4 random drawings, then I have to add the probability of drawing one five plus the probability of drawing two fives, plus ..., all the way up to the probability of drawing 4 fives (in every single draw, I draw a 5).

Hint: Begin by finding the probability of drawing one five, in an n amount of draws. Please show some work and give us some information on your math background when you return.
 
The results when interpreting the problem in the following two ways are the same:

1. Choose an n amount of balls, and write down the entire sequence. Find the probability of choosing a 5, so you have to add all the probabilities (choosing 2 5's, 3 5's, 4 5's, etc. anywhere in the sequence).

2. Choose balls one by one and you are successful when you draw a 5. Stop drawing when you get a 5. The probability would be to add the probability of choosing a 5 on the first draw, plus the prob. of choosing on the second draw, etc.

Can someone help give an intuitive explanation for why the probabilities are the same?

Thanks
 
Last edited:
Hi! I really don't know how to get the answer to this question:

An urn contains 9 balls numbered 1 to 9. A ball is drawn with replacement an indefinite number of times. The number appearing on each draw is noted down in a sequence. What is the length of the shortest sequence such that the probability of getting at least one 5 is at least 80%?
Can you solve \(\displaystyle 1-\left(\frac{8}{9}\right)^N\ge 0.8~?\)
 
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