This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 178

2022 JHMT HS, 7
Tags: expected value
A spider sits on the circumference of a circle and wants to weave a web by making several passes through the circle's interior. On each pass, the spider starts at some location on the circumference, picks a destination uniformly at random from the circumference, and travels to that destination in a straight line, laying down a strand of silk along the line segment they traverse. After the spider does $2022$ of these passes (with each non-initial pass starting where the previous one ended), what is the expected number of points in the circle's interior where two or more non-parallel silk strands intersect?

2015 CCA Math Bonanza, L3.1
Tags: probability , expected value
Bhairav the Bat lives next to a town where $12.5$% of the inhabitants have Type AB blood. When Bhairav the Bat leaves his cave at night to suck of the inhabitants blood, chooses individuals at random until he bites one with type AB blood, after which he stops. What is the expected value of the number of individuals Bhairav the Bat will bite in any given night? [i]2015 CCA Math Bonanza Lightning Round #3.1[/i]

2009 Princeton University Math Competition, 7
Tags: probability , expected value
We randomly choose 5 distinct positive integers less than or equal to 90. What is the floor of 10 times the expected value of the fourth largest number?