Probability Studio
Final round
Ten problems from the whole studio, in no particular order. Nothing tells you which chapter they belong to: choosing the right picture is the test. 0 of 10 solved
The last ball
A bag holds 5 red and 5 blue balls. You draw them all, one at a time, without looking. What is the probability that the last ball is red?
First head wins
Two players take turns flipping a coin, and the first to flip heads wins. What is the probability that the player who flips first wins?
Runs of coins
A coin is flipped 10 times. A run is a block of equal flips in a row, so HHTHH has three runs. What is the expected number of runs?
A rare condition
2% of people have a condition. A test catches 90% of those who have it and wrongly flags 5% of those who don't. You test positive. What is the chance you have the condition? (Two decimals.)
Only even rolls
You roll a die until the first 6. Given that every roll you made was even, what is the expected number of rolls?
A triangle round the centre
Three points are chosen at random on a circle. What is the probability that the triangle they form contains the centre?
A pair in five cards
Five cards are dealt from a shuffled deck. What is the probability that at least two of them share a rank? (Two decimals.)
No two heads in a row
A coin is flipped 10 times. What is the probability that no two heads come up in a row?
Every face
A die is rolled until every face has appeared at least once. What is the expected number of rolls? (One decimal.)
The first ace
A shuffled deck is turned over one card at a time. What is the expected position of the first ace?