Algebra Problems, Math Problems

Problem of the Day: 3/7/13

The area of a rectangle can be expressed as 3x^2-11x+6. What is the perimeter of this rectangle in terms of x?

Solution to yesterday’s problem:

If the frog has an equal probability of landing on any lily pad, and he can land on two possible pads (he cannot jump vertically and land on the same lily pad), then the probability of him landing on a particular pad is \frac{1}{2}. Therefore, the probability of any permutation of three jumps is \frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}.

Let’s make a tree diagram of all the possible ways he could jump. Say he started on lily pad 1. Here it is:

20130307-072009.jpg

Notice that there are two ends of the branches that have a one, which is the pad the frog started on. So the probability of any of these two permutations occurring is \frac{2}{8}, or \frac{1}{4}.

Advertisements

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 )

Twitter picture

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

Facebook photo

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

Google+ photo

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

Connecting to %s