Least number of coin tosses for at least one head with probability above a value

The same question, asked 2 times: 10 May 2023 S2*, 14 May 2026 S2. Every wording below, oldest first.

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Question 1
10 May 2023 S2
111 $Minimum number of times a fair coin must be tossed, so that the probability of getting at least one head, is more than 99% is$
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Question 2
14 May 2026 S2
99 $0.8$
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