Source: Problem prompts adapted from Ace the Data Science Interview — Chapter 5 Medium set (Huo & Singh). Solutions and explanations here are original for this course.
Ten more probability interview questions, one tier up from the easy set. Same tile format: click a problem, enter a numeric answer (at most 2 decimals). Green tiles are ones you've solved, and progress is saved in this browser. If you check an answer wrong twice, the official answer and explanation are revealed automatically.
Hints: these lean more on recursive/recurrence setups (waiting games, series-to-a-lead) and on translating a "generate fair odds" or "geometric" story into an equation before computing.
0/10 solved
5.19Morgan Stanley
A number k from 1–6 is chosen. Players A and B take turns rolling a fair die (A first), and whoever first rolls k wins 100 dollars. How much (in dollars) should A be willing to pay for the right to go first?
Enter a number (at most 2 decimal places).
5.20Airbnb
You have a coin with an unknown, possibly unfair bias p toward heads. Von Neumann's trick flips it twice: call the result "heads" on HT, "tails" on TH, and discard/reflip on HH or TT — this is fair for any p. For p=0.3, what is the probability that a single two-flip attempt produces a usable (non-discarded) result?
Enter a number (at most 2 decimal places).
5.21SIG
A cube is cut into a 3×3×3 grid of 27 unit cubes after all 6 outer faces were painted green. You pick one of the 27 small cubes at random and see 5 of its faces are white (the 6th, hidden "bottom" face is unknown). What is the probability the bottom face is also white?
Enter a number (at most 2 decimal places).
5.22Goldman Sachs
A stick of length 1 is broken at two independent, uniformly random points into three pieces. What is the probability the three pieces can form a triangle?
Enter a number (at most 2 decimal places).
5.23Lyft
You flip a fair coin repeatedly. What is the probability that the pattern HHT appears before the pattern HTT?
Enter a number (at most 2 decimal places).
5.24Uber
A fair coin is tossed twice. What is P(both heads∣at least one toss was heads)?
Enter a number (at most 2 decimal places).
5.25Facebook
Three ants sit at the corners of an equilateral triangle. Each independently picks one of the two directions along the triangle's edges and starts walking. What is the probability that no two ants ever meet?
Enter a number (at most 2 decimal places).
5.26Robinhood
A coin with P(heads)=p=0.3 is tossed n times. The probability of an even number of heads follows Pn=(1−p)Pn−1+p(1−Pn−1) with P0=1. What is P4?
Enter a number (at most 2 decimal places).
5.27Citadel
Alice and Bob play rounds until one of them is two rounds ahead; that player wins the series. Alice wins each round with probability p=0.4. What is the probability that Bob wins the series?
Enter a number (at most 2 decimal places).
5.28Google
You draw three independent values uniformly from (0,2). What is the probability that their median exceeds 1.5?