Question

is there enough evidence? (option 1 of 4)
two friends, tom and jerry, were flipping a coin to see who was going to pay for lunch. the coin was flipped and landed on tails so jerry won. tom argued that particular coin was not fair and is more likely to land on tails. so they flipped the coin 10 total times, 6 of which were tails compared to 4 heads.
\see,\ tom said, \that coin isnt fair, it lands on tails 60% of the time.\

o way,\ says jerry \6 out of 10 is not enough proof to say the coin is not fair.\
if you agree with tom, explain why. if you agree with jerry, how many flips would it take to convince you that the coin is not fair? in other words, what evidence would need to exist for you be convinced that the coin is not fair?

Explanation:

Step1: Analyze the sample size

A sample of 10 coin flips is extremely small. In probability and statistics, small sample sizes are more likely to deviate from the expected theoretical probability (for a fair coin, \(P(\text{heads})=P(\text{tails}) = 0.5\)). Random chance can more easily cause non - representative results in a small sample.

Step2: Consider the law of large numbers

The law of large numbers states that as the number of trials \(n\) increases, the sample proportion \(\hat{p}\) (in this case, the proportion of tails) gets closer to the True population proportion \(p\). For a fair coin \(p = 0.5\). A common rule - of - thumb (though not a strict statistical rule) for a more reliable estimate could be \(n\geq 30\). With \(n = 30\), if the proportion of tails is significantly different from \(0.5\) (using a hypothesis test, for example, a one - sample proportion test with a significance level like \(\alpha=0.05\)), we can start to have more confidence in concluding that the coin is not fair.

Answer:

Agree with Jerry. A sample of \(n = 10\) is too small. A sample size of at least \(n = 30\) (a common starting point for more reliable statistical inferences) would be needed. If, after \(n = 30\) flips, the proportion of tails is, say, greater than \(0.6\) (and a hypothesis test for a fair coin gives a p - value less than \(0.05\)), it would be more convincing that the coin is not fair.