Calculating Confidence: Solving a MIT Probability Problem

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SUMMARY

The discussion centers on calculating the number of tosses required to achieve 95% confidence in identifying which of two coins was chosen: a fair coin and a biased coin with a 3/4 probability of heads. Participants recommend using the test for comparing two proportions to approach the problem. Key concepts include random variables, expectation, and distributions, which are essential for understanding the statistical methods involved. While the exact minimum value of tosses (n) is not calculated, the focus remains on the methodology for determining confidence levels in probability scenarios.

PREREQUISITES
  • Understanding of random variables
  • Knowledge of expectation in probability
  • Familiarity with statistical distributions
  • Experience with hypothesis testing, specifically comparing two proportions
NEXT STEPS
  • Study the test for comparing two proportions in detail
  • Learn about confidence intervals and their calculations
  • Explore the concept of hypothesis testing in statistics
  • Investigate the implications of sample size on statistical confidence
USEFUL FOR

Students preparing for statistics exams, educators teaching probability concepts, and data analysts working with hypothesis testing and confidence intervals.

birderfox
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Problem:

We have two coins: one is fair and the other coin is a coin that produces heads with probability 3/4. One of the two coins is picked and this coin is tossed n times. Explain how to calculate the number of tosses to make us 95% confident which coin was chosen. You do not have to calculate the minimum value of n, though we would be pleased if you did.

So this problem is a practice problem for a test. I have been trying to solve it for a few hours now and I am kind of stuck. We have been studying random variables, expectation and distributions. Any of you guys have any idea of how to approach this?

Thanks
 
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birderfox said:
Problem:

We have two coins: one is fair and the other coin is a coin that produces heads with probability 3/4. One of the two coins is picked and this coin is tossed n times. Explain how to calculate the number of tosses to make us 95% confident which coin was chosen. You do not have to calculate the minimum value of n, though we would be pleased if you did.

So this problem is a practice problem for a test. I have been trying to solve it for a few hours now and I am kind of stuck. We have been studying random variables, expectation and distributions. Any of you guys have any idea of how to approach this?

Thanks

Use the test for comparing two proportions.
 

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