The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-stat

Topic: [ap-stat] RE: Spread of an epidemic
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
pat ballew

Posts: 334
Registered: 12/3/04
[ap-stat] RE: Spread of an epidemic
Posted: Nov 1, 2000 7:14 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

If I understand the question, the only way the virus will survive to infect
everyone is if the random selection never repeats a monk. thus the
probability is just the probability that you pick 8 numbers in a row at
random from (1-8) and never repeat a value...

The initial monk is monk zero, and we assume he WILL infect someone so the
probability of one transmission is P(1)=1

The probability of a second transmission is the chance that monk one will
visit one of the six monks other than monk zero, hence p(2)= 6/7...

The probability of a third transmission is the chance that monk one infected
someone (monk 2) times the probability that he found one of the five
remaining non-immune monks out of the seven other monks ... hence

I think from here the method is clear if I am really understanding the

The probability then, that the epidemic ends after one infection is 1/7,
after two infections is 6/7*2/7, --- P(2) times NOT a third...
after three infections is 6/7 * 5/7 * 3/7 ....
and the probability that it infects everyone is 6/7*5/7*4/7*4/7*2/7*1/7

I think I did that right,
but as soon as I push send I'll find something.... Hmmmm.... well here

Pat Ballew,
Misawa, Jp

"Statistics means never having to say you're certain."

Math Words & Other Words

The Mathboy's page

-----Original Message-----
From: Mark Fountain [mailto://]
Sent: Thursday, November 02, 2000 7:25 AM
To: AP Statistics
Subject: [ap-stat] Spread of an epidemic

Hi, folks.

This is a question about YMM Special Problem 5A, The Spread of an epidemic.
The setup is like this. There are 8 monks and one is infected with a 100%
contagious 24-hour virus. While contagious, the contagious monk randomly
visit one of the other monks. Twenty-four hours later he is immune but the
new carrier visits another randomly chosen monk. If that monk is already
immune, the virus will die out; if not, the cycle continues. Will the
virus die out before everyone is infected?

The task is to setup a similation and repeat it several times. However,
one group is really hung up on the theoretical probability of this
happening. Here's my best guess so far. There are 8! different orders
that would infect every monk. There are 8^8 different ways to choose 8
random numbers since we have to allow replacement. So the probability is
8!/(8^8) = .002ish. What think you? I'm really not very confident with
probability questions.

Thanks for your input.
Sue Fountain

You are currently subscribed to ap-stat as:
To unsubscribe send a blank email to
Frequently Asked Questions(FAQ) Site is at
AP Statistics Archives are at

You are currently subscribed to ap-stat as:
To unsubscribe send a blank email to
Frequently Asked Questions(FAQ) Site is at
AP Statistics Archives are at

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.