Community Category: Math

If you throw a fair coin 1000 times, what is the expected number of occurrences of 5 heads followed by 5 tails?

What is the expected number of tosses until you get five heads in a row with a fair coin?

Suppose there is an ant in one corner of a cube. Every second, the ant moves from one corner to an arbitrary neighboring one along one of the three available edges. What is the expected time until the ant comes back to the starting corner?

Two people are taking turns throwing a hundred sided die. The game continues until someone throws a number larger than the number thrown by the opponent on the previous turn. What is the probability that the person who throws first wins the game?

Example: 4 – 3 – 3 – 2 – 5 => First player wins
Example: 6 – 3 – 2 – 1 – 1 – 4 => Second player wins

If you break a stick into three pieces, what is the probability that they can form a triangle?