A nice probability coincidence today

This morning my older son and I talked through the following problem from the 2003 AMC 10b:

Screen Shot 2018-02-15 at 7.11.31 PM.png

It turned out that an arithmetic problem is what led to his confusion on this problem, but discussing this problem was a nice opportunity to talk about discrete probability. At the end of our conversation I told him to always remember the underlying idea in discrete probability is simple -> count the cases that work and then count the total cases. It may not always be so easy to do, but it really is all that you have to do to solve the problem.

After he went off to school I this problem posted on Twitter:

This is a terrific problem, and it is really tempting to try to break the problem into pieces and essentially to try to solve it with recursion.

But remember the simple little idea I told my son -> count the cases that work and count the total cases. You’ll find a delightful solution to the problem!

Advertisements

Comments

One Comment so far. Leave a comment below.
  1. While looking to check my solution I found that this is from the 2003 AMC 10A test 🙂

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: