Advanced Placement (AP) High School

suppose a coin is fair (p=1/2 for heads or tails). How many times would you have to flip the coin to get the standard error down to 1%

Answers

Answer 1

The standard error of a coin flip is the standard deviation of the probability of heads, which is equal to the square root of the probability of heads times the probability of tails. In this case, the probability of heads is 1/2 and the probability of tails is also 1/2, so the standard error is equal to the square root of (1/2)(1/2) = 1/4.

To get the standard error down to 1%, you would need to flip the coin a sufficient number of times so that the standard error is less than or equal to 1/100. In other words, you would need to flip the coin until the standard error is less than or equal to 1% of the probability of heads.

To solve for the number of coin flips required, you can use the following equation:

number of coin flips = (standard error / probability of heads)^2

Substituting the values for the standard error and probability of heads, we get:

number of coin flips = (1/100 / 1/2)^2 = (1/50)^2 = 1/2500

To express this result in terms of the number of coin flips, we need to find the smallest integer value greater than or equal to 1/2500. This value is approximately 400, so you would need to flip the coin approximately 400 times to get the standard error down to 1%.

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