Events and Probability Spaces · Theory Problems

Lesson 3

Nikolai Chukhin · Alexander S. Kulikov

Optional Problems.

  1. (20 points) Two people play: flip a biased coin twice (the probability of heads is \(p \in (0,1)\)); if the result is HT, the first wins; if TH, the second wins; if HH or TT, start over. Find the probability that the first player wins.
    Hint:
    Let \(x\) denote the desired probability and write a recurrence describing it.
  2. (25 points) One flips a coin until \(k\) consecutive heads. The probability of head is \(p\in(0,1)\). How many flips on average are needed for that to happen?