Problem

6. What is the least number of times you need to toss a fair coin so that the probability of having at least one tail is greater than 0.9999 ?

Answer

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Answer

\(\boxed{14}\) is the least number of times you need to toss a fair coin so that the probability of having at least one tail is greater than 0.9999.

Steps

Step 1 ：Let n be the number of tosses. The probability of getting all heads in n tosses is \((\frac{1}{2})^n\). We want to find the smallest n such that:

Step 2 ：\(1 - (\frac{1}{2})^n > 0.9999\)

Step 3 ：Solve this inequality step by step:

Step 4 ：n = 14

Step 5 ：\(\boxed{14}\) is the least number of times you need to toss a fair coin so that the probability of having at least one tail is greater than 0.9999.

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