(Probability) Call His Bluff

It's poker night and the game is Texas Holdem. Now, get your poker face on and crunch those numbers!

You're sitting in the final round of betting with pocket rockets (a pair of Aces) in your hand. On the table there is an 8 of diamonds, 2 of hearts, 3 of spades, 4 of clubs, and the dealer just revealed a 6 of clubs. Two of your opponents just folded, and one is betting as if he had a 5 to complete the straight on the table.

What is the probability that your opponent has a 5 in his hand?
Here's a refresher on Texas Holdem

(Materials) Steel Hanging From The Ceiling

Part 2 of 2 - Let's build on yesterday's problem.

Why do we bother finding out how much something deforms, when it's stress that gives us a measure of whether something will fail?

In the real world, directly measuring stress can be pretty difficult. It's much easier to stick a strain gauge to the interested area of a part to measure the amount something deforms. From there we can use an equation to relate strain to stress. We go into this more in today's solution (after you try solving the problem of course!). 

You hang a steel cylinder from the ceiling. At 3 various points, you decide to hang some heavy stuff. Young's Modulus of steel is 210 GPa.

How much will the length of the steel cylinder change?

      0.19 mm
      0.56 mm
      0.66 mm
      0.98 mm

(Materials) Tug of War Over an Aluminum Rod...

You and your friend are playing tug-of-war over an aluminum rod that you each want for yourself.

The diameter of this rod is 25mm, and the standard elasticity of aluminum is 69 GPa.

How much are you guys elongating the rod by fighting over it?

      0.03 mm
      0.01 mm
      0.3 mm

The Power of Compound Interest (Economics Pt 2 of 2)

In part 1, you learned how to calculate the Future Value of a “single-deposit” investment that compounds over time.  To recap, if you presently invest any “single” sum (PV), at a certain rate of return (r), across (n) time periods… that will yield a future return (FV) exhibited by the following equation:

Today, we are going to advance this concept by adding in the ability to make “continual-deposit” installments. After all, it isn't just by compound interest that Aunt Bessie got rich, but by saving!  

So let's say that you make it a goal to put away just $300 every month. You deposit that into a 401(k) retirement account yielding 7% per year, and automatically reinvests returns to “compound monthly.” After 35 years of doing this, how much money would you have? 

(NOTE: The math is a bit more complex. So if you can’t figure it out, just learn from the solution!)