Find maximum n for P(X > n) > threshold

Questions asking for the largest n such that the probability of requiring more than n trials exceeds or stays above a given threshold (e.g., P(X > n) > 0.05).

1 questions

CAIE FP2 2019 June Q6
6 A fair six-sided die is thrown until a 3 or a 4 is obtained. The number of throws taken is denoted by the random variable \(X\).
  1. State the mean value of \(X\).
  2. Find the probability that obtaining a 3 or a 4 takes exactly 6 throws.
  3. Find the probability that obtaining a 3 or a 4 takes more than 4 throws.
  4. Find the greatest integer \(n\) such that the probability of obtaining a 3 or a 4 in fewer than \(n\) throws is less than 0.95.