Discrete Mathematics
# Geometric Probability

A number is uniformly chosen from $[0.15, 0.25]$. It was rounded to two decimal places and then to one decimal place. The probability that the final value is $0.2$ is $X \%$. What is $X?$

**Assumption:** Use rounding "half away from zero". That is, if the number is equally far from the two closest numbers, choose the one away from zero. For example, 2.5 is equally far from 2 and 3, so round 2.5 to 3.

7 Sumo Wrestlers are eager to hop onto the merry-go-round. However, if they were to be contained within the same half of the merry-go-round, then their combined weight would cause the merry-go-round to topple.

If all 7 Sumo Wrestlers were to hop onto the merry-go-round at a random point along the circumference of the merry-go-round, what is the probability (to 3 decimal places) that the merry-go-round will topple?