Probability Interview Questions

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Last updated Nov 2026

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Two pieces are placed at random on different squares of an 8 by 8 board. What is the probability that they share neither a row nor a column?
5 years ago
A and B start at opposite corners of a 4x4 grid and step towards each other's corner at random each second. What is the probability they ever share a position?
2 years ago
32 teams of distinct strength are randomly seeded in a knockout where the stronger team always wins. What is the probability the final is the best against the third best?
2 years ago
You want to bake 5 cookies for a friend and can make 4 flavours. How many combinations of cookies can you bake?
10 months ago
A spinner lands in three regions with probabilities 1/5, 3/10 and 1/2. What is the expected number of spins until it has landed in two different regions?
10 months ago
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You choose 6 numbers at random from the first 35 positive integers. What is the expected number of consecutive pairs among them? (10, 11 and 12 would count as two pairs.)
10 months ago
Random variables a, b, c satisfy corr(a,b) = 1/2 and corr(b,c) = 1/2. What range can corr(a,c) take?
11 hours ago
Four variables have all pairwise correlations 1/2 except corr(a,d). What range can corr(a,d) take? Compute it in code.
11 hours ago
One of 100 doors hides a prize. You pick a door, then the host opens 98 of the others, all empty, and offers a switch. Should you switch, and what is your chance of winning?
11 hours ago
Two bullets sit at random in a six-chamber revolver and the first pull is empty. What is the probability the next pull fires? What if the bullets are known not to be adjacent?
11 hours ago
X and Y are iid standard normal. What is P(X > 3Y | X > 0)?
11 hours ago
Nine cats and eight dogs are placed at random in a row of 17 places. What is the expected number of adjacent pairs made of one cat and one dog?
11 hours ago
X is the sum of 100 rolls of a fair die and Y is the number of heads in 600 fair coin flips. What is P(X > Y)?
6 years ago
Two three-digit numbers, each from 100 to 999, are chosen independently and uniformly at random. What is the probability that their absolute difference is a two-digit number?
2 years ago
You flip 8 fair coins. What is the probability that the same face comes up at least three times in a row at some point?
2 years ago
Thirteen cards are dealt from a standard deck. What is the probability that none is an ace?
2 years ago
Roll three dice. What is the probability that some subset of them (one, two or all three dice) sums to exactly 5?
2 years ago
A bag holds 10 red, 10 yellow and 10 blue balls. You draw three balls without replacement. What is the probability that the three balls are all of different colours?
2 years ago
Start with 30 and roll a die 10 times; each roll adds 1 or subtracts 1 with probability 1/2. What is the expected final score?
2 years ago
You must buy one unit at each of n times, at a Uniform(a, b) market price you see first or from a broker at fixed price p, at most k times. Compute the expected optimal cost.
2 years ago

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Probability Interview Questions

Two pieces are placed at random on different squares of an 8 by 8 board. What is the probability that they share neither a row nor a column?

A and B start at opposite corners of a 4x4 grid and step towards each other's corner at random each second. What is the probability they ever share a position?

32 teams of distinct strength are randomly seeded in a knockout where the stronger team always wins. What is the probability the final is the best against the third best?

You want to bake 5 cookies for a friend and can make 4 flavours. How many combinations of cookies can you bake?

A spinner lands in three regions with probabilities 1/5, 3/10 and 1/2. What is the expected number of spins until it has landed in two different regions?

You choose 6 numbers at random from the first 35 positive integers. What is the expected number of consecutive pairs among them? (10, 11 and 12 would count as two pairs.)

Random variables a, b, c satisfy corr(a,b) = 1/2 and corr(b,c) = 1/2. What range can corr(a,c) take?

Four variables have all pairwise correlations 1/2 except corr(a,d). What range can corr(a,d) take? Compute it in code.

One of 100 doors hides a prize. You pick a door, then the host opens 98 of the others, all empty, and offers a switch. Should you switch, and what is your chance of winning?

Two bullets sit at random in a six-chamber revolver and the first pull is empty. What is the probability the next pull fires? What if the bullets are known not to be adjacent?

X and Y are iid standard normal. What is P(X > 3Y | X > 0)?

Nine cats and eight dogs are placed at random in a row of 17 places. What is the expected number of adjacent pairs made of one cat and one dog?

X is the sum of 100 rolls of a fair die and Y is the number of heads in 600 fair coin flips. What is P(X > Y)?

Two three-digit numbers, each from 100 to 999, are chosen independently and uniformly at random. What is the probability that their absolute difference is a two-digit number?

You flip 8 fair coins. What is the probability that the same face comes up at least three times in a row at some point?

Thirteen cards are dealt from a standard deck. What is the probability that none is an ace?

Roll three dice. What is the probability that some subset of them (one, two or all three dice) sums to exactly 5?

A bag holds 10 red, 10 yellow and 10 blue balls. You draw three balls without replacement. What is the probability that the three balls are all of different colours?

Start with 30 and roll a die 10 times; each roll adds 1 or subtracts 1 with probability 1/2. What is the expected final score?

You must buy one unit at each of n times, at a Uniform(a, b) market price you see first or from a broker at fixed price p, at most k times. Compute the expected optimal cost.

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