Calculating Confidence: Solving a MIT Probability Problem

In summary: First, calculate the expected proportion of heads for each coin. Then, use the formula for the standard error to calculate the margin of error. Finally, use the margin of error to determine the confidence interval and compare it to the expected proportion to determine which coin was chosen.
  • #1
birderfox
1
0
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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  • #2
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.
 

What is the "MIT Probability Problem"?

The "MIT Probability Problem" is a famous mathematical problem that was first proposed by the Massachusetts Institute of Technology (MIT) in the 1960s. It is a probability puzzle that challenges individuals to use their mathematical and logical skills to solve a seemingly simple problem.

What is the goal of the "MIT Probability Problem"?

The goal of the "MIT Probability Problem" is to accurately predict the outcome of a series of coin flips. The problem involves a hypothetical game where an individual must correctly choose the outcome of 100 coin flips in order to win a prize.

What makes the "MIT Probability Problem" difficult to solve?

The "MIT Probability Problem" is difficult to solve because it challenges individuals to think beyond the obvious solution. While the problem may seem simple at first glance, it requires a deep understanding of probability and strategic thinking in order to come up with an accurate prediction.

What are some strategies for solving the "MIT Probability Problem"?

Some strategies for solving the "MIT Probability Problem" include using mathematical equations, creating a probability tree, and applying logical reasoning. It is also important to consider any additional information given in the problem and to think creatively about potential solutions.

Why is the "MIT Probability Problem" important in the field of science?

The "MIT Probability Problem" is important in the field of science because it challenges individuals to think critically and use mathematical and logical skills to solve a problem. This type of problem-solving is essential in many scientific fields and can help researchers develop innovative solutions to complex problems.

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