Question:
A fair coin is tossed \(n\)-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of \(n\) is ______________.
A fair coin is tossed \(n\)-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of \(n\) is ______________.
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\(P(\text{at least one head})=1-\left(\frac12\right)^n\ge0.9\).
Updated On: Nov 4, 2026
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Correct Answer: 4
Solution and Explanation
\(P(\text{at least one head})=1-\left(\frac12\right)^n\ge0.9\Rightarrow\left(\frac12\right)^n\le0.1\Rightarrow2^n\ge10\).
\(2^3=8\lt10\), \(2^4=16\ge10\). Minimum \(n=4\).
Answer: 4
\(2^3=8\lt10\), \(2^4=16\ge10\). Minimum \(n=4\).
Answer: 4
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