MathDB

15

Part of 2014 BMT Spring

Problems(2)

2014 BMT Team 15

Source:

1/6/2022
Suppose a box contains 2828 balls: 11 red, 22 blue, 33 yellow, 44 orange, 55 purple, 66 green, and 77 pink. One by one, each ball is removed uniformly at random and without replacement until all 2828 balls have been removed. Determine the probability that the most likely “scenario of exhaustion” occurs; that is, determine the probability that the first color to have all such balls removed from the box is red, that the second is blue, the third is yellow, the fourth is orange, the fifth is purple, the sixth is green, and the seventh is pink.
combinatorics
BMT 2014 Spring - Individual 15

Source:

1/22/2022
Albert and Kevin are playing a game. Kevin has a 10%10\% chance of winning any given round in the match. If Kevin wins the first game, he wins the match. If not, he requests that the match be extended to a best of 33. If he wins the best of 33, he wins the match. If not, then he requests the match be extended to a best of 55, and so forth. What is the probability that Kevin eventually wins the match? (A best of 2n+12n+ 1 match consists of a series of rounds. The first person to reach n+1n + 1 winning games wins the match)
combinatorics