Solve estimation and probability brainteasers

Answer the following independent brainteaser questions. State any assumptions you need. 1) **Tile a floor**: A floor is **15 ft × 20 ft**. You will cover it with square tiles of area **1 square yard** each. Approximately how many tiles are needed? 2) **Doubling account**: An account starts with **$1000** and **doubles every year**. How much is in the account after **20 years**? 3) **Estimate Earth–Moon distance**: Sitting by a window and looking at the Moon, estimate the distance from you to the Moon using reasonable “back-of-the-envelope” reasoning. 4) **Stones in a boat**: A boat is floating in a lake with some stones in it. You throw the stones into the lake. Does the lake’s water level rise, fall, or stay the same? 5) **Probability of even product**: There are **two boxes**. Each box contains three cards labeled **1, 2, 3** (one of each). You draw one card from each box (uniformly at random). What is the probability that the **product** of the two numbers is **even**? 6) **Uncompressed 1080p movies on a 2 TB drive**: Approximately how many **uncompressed 1080p** movies can fit on a **2 TB** hard drive? Clearly state assumptions (frame rate, color depth/bytes per pixel, movie length, TB definition). 7) **Nested squares area**: Three squares are “nested” one inside another (concentric), with each inner square formed by connecting the **midpoints** of the sides of the previous square. If the **innermost** square has area \(A\), what is the area of the **outermost** square?