Calculating Confidence: Solving a MIT Probability Problem

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To determine which coin was chosen with 95% confidence, one can use statistical methods for comparing two proportions. The problem involves tossing a fair coin and a biased coin (with a 3/4 probability of heads) and analyzing the outcomes. By calculating the expected number of heads from each coin and applying a hypothesis test, one can establish the number of tosses needed to differentiate between the two coins. The discussion emphasizes the importance of understanding random variables, expectation, and distributions in solving the problem. Ultimately, the approach hinges on statistical testing to achieve the desired confidence level.
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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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