Source: Problem prompts adapted from Ace the Data Science Interview — Chapter 5 Easy set (Huo & Singh). Solutions and explanations here are original for this course.
Eighteen classic probability interview questions, the easy tier. Medium and hard tiers continue with the same tile format.
Use the numbered tiles like an exercise set — click a problem, enter a numeric answer (at most 2 decimals; path counts are integers). 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: identify the model first (binomial series, Bayes, counting paths, waiting games), then compute.
0/18 solved
5.1Google
Two teams play a best-of-7 series (first to 4 wins). Each game is an independent coin flip — each team has probability 1/2 of winning any game (no draws). What is the probability the series goes the full 7 games?
Enter a number (at most 2 decimal places).
5.2JP Morgan
You roll a fair six-sided die three times. What is the probability of getting two sixes in a row (on rolls 1–2 and/or rolls 2–3)?
Enter a number (at most 2 decimal places).
5.3Uber
You roll three fair dice one after another. What is the probability that the three numbers are strictly increasing?
Enter a number (at most 2 decimal places).
5.4Zenefits
A deck has 100 cards labeled 1 through 100. You draw two cards at random without replacement. What is the probability that one number is exactly double the other?
Enter a number (at most 2 decimal places).
5.5JP Morgan
In 3D space, how many shortest paths are there from (0,0,0) to (3,3,3) if each step increases exactly one coordinate by 1 (only “up”, “right”, or “forward”)? Enter the integer count.
Enter a number (at most 0 decimal places — integer).
5.6Amazon
One in a thousand people have a disease. A test is correct 98% of the time when the person has the disease, and has a 1% false-positive rate when they do not. Someone tests positive. What is the probability they have the disease?
Enter a number (at most 2 decimal places).
5.7Facebook
There are two coins: one fair (H/T) and one double-tailed. You pick a coin at random, flip it five times, and see TTTTT. What is the probability you are flipping the unfair coin?
Enter a number (at most 2 decimal places).
5.8Goldman Sachs
Players A and B take turns flipping a coin with P(heads)=p; first heads wins. A starts. For the fair case p = 0.5, what is the probability that A wins?
Enter a number (at most 2 decimal places).
5.9Microsoft
Prior probability of rain in Seattle on a given day is 0.25. Three friends each independently say it is rainy; each lies with probability 1/3. What is the probability it is actually rainy given all three reports?
Enter a number (at most 2 decimal places).
5.10Bloomberg
You draw a circle and choose two chords uniformly at random (via four random endpoints on the circumference). What is the probability that the two chords intersect inside the circle?
Enter a number (at most 2 decimal places).
5.11Morgan Stanley
You and a friend toss a fair coin until HH or TH appears. You win on HH; your friend wins on TH. What is the probability that you win?
Enter a number (at most 2 decimal places).
5.12JP Morgan
You may roll a fair 6-sided die up to twice and can stop after the first roll. Your payoff is the face value of the final roll (in dollars). Under optimal play, what is the expected value of the game (how much are you willing to pay)?
Enter a number (at most 2 decimal places).
5.13Facebook
90% of raters are diligent: they mark content spam with probability 0.20 (so “good” with 0.80). The other 10% never mark spam (always “good”). Labels are independent. A rater marks four pieces as good. What is the probability this rater is diligent?
Enter a number (at most 2 decimal places).
5.14D.E. Shaw
A couple has two children. You learn that at least one is a boy. Assuming each child is independently boy/girl with equal probability, what is the probability both are boys?
Enter a number (at most 2 decimal places).
5.15JP Morgan
A desk has 8 drawers. With probability 1/2 a letter was placed uniformly at random in one drawer; with probability 1/2 there is no letter at all. You open the first 7 drawers and all are empty. What is the probability the 8th drawer contains the letter?
Enter a number (at most 2 decimal places).
5.16Optiver
Tennis deuce: play until one player leads by two points. Player 1 wins each point with probability 0.60 (independently). What is the probability player 1 wins the game from deuce?
Enter a number (at most 2 decimal places).
5.17Facebook
A deck has 50 cards: 5 colors × numbers 1–10 (one card per color-number pair). You draw two cards at random. What is the probability they have different colors and different numbers?
Enter a number (at most 2 decimal places).
5.18SIG
You roll ten fair six-sided dice at once. What is the probability that the sum of the top faces is divisible by 6?