Transcript warmup

Random Warmup
Finding a Short Story
• Suppose a book of short stories has both
shorter short stories and longer short
stories.
• Their order within the book is random.
• You want to pick a random story to read,
but you would prefer it is a shorter one.
Finding a Short Story
• Two Strategies
– Strategy #1: Flip to a random page, back up
to the beginning of that story, and start
reading
– Strategy #2: Flip to a random page, go
forward to the beginning of the next story, and
start reading
• (Go to first story if you are at the end of the book)
• Does it matter which strategy you use?
To What Kind of Story Is a Random
Page Likely to Belong
• To be concrete, suppose there are 20 stories
– 10 of them are 10 pages long
– 10 of them are 20 pages lon
• So book is 300 pages long
• The Expected #pages in the story on a
random page is (200∙20+100∙10)/300 = 16.7
• When you pick a random page, it will belong
to a longer story with probability 2/3
The Second Strategy Works Better!
• Strategy #1 will have you reading a longer
story with probability 2/3 and a shorter
story with probability 1/3
• Strategy #2 will take you to the beginning
of a random STORY
• So Strategy #2 will take you to the
beginning of a longer story with probability
½ and a shorter story with probability ½
FINIS