What Are The Odds?

This morning I woke up early (6:30 AM) to go to the gym in the Commons Center that opens at 7 AM. I was one of the first five people there, because I knew that once it reached 7 AM, the gym would be flooded with VSA students. When I got there, I waited for the gym to open. 7 o'clock came and went, and no one came to unlock the gym. By 7AM  there were 25 people waiting. The gym so small that there aren't even 25 machines. Someone went down to the front desk to ask about opening it, but there was no one there. Most people waited until 7:15, and then left. I waited until 7:30 to be safe, but no one came. This was not a good way to start my morning: Getting up early for nothing. The rest of my day went better though.

Today's Puzzler was another dice puzzle. Just like last time, five dice are rolled. This time the riddle is "Polar Bears. They fish in pairs. They sit around and fish, through holes in the ice." Unfortunately, I could not find a website with this game like with the Rose Petal one. In fact, Dawson used the Rose Petal game for the dice, but confirmed the answers verbally. There are two parts to the question: How many bears, and how many fish. The bears are easy. They sit around a center dot, just like the pedals around the rose. The fish are more tricky. Since they are fishing through holes in the ice (center dots) the fish are on the other side of the die. Since opposite sides of the die add up to 7, 1's have 6 fish, 3's have 4 fish, and 5's have 2 fish. 2's, 4's, and 6's do not affect the number of bears or fish. We spent 45 minutes on this Puzzler. The first few people finally got it after about 30 minutes.

Next we did independent study. I was able to finish my problems, and take my first quiz. Unfortunately, I got 3 out of 5. I knew I got one of them wrong, but the second one was a silly mistake. From my mistakes, Dawson told me he could tell I knew what I was doing, but just was a little too quick. He said he would give me the second quiz (the easier one) the next time we did independent study. Next we did lecture/discussion. Today's topic was using Combinatorics to calculate probability. We calculated the odds of pulling out three chips from an urn containing 8 chips numbered 1-8, such that the largest number was 5. We divided this into 4 parts. First was the numbers we did not want (6, 7, 8) we wanted to choose 0 of those 3. Second was the five. There was only one, so it was one choose one. Then we could pick 2 of the 4 remaining numbers. All these statements have to be true to satisfy the statement, so we multiply them together to get the number of "favorable" outcomes, and divided it by the total number of outcomes (8 choose 3). This turned out to be 0.7%. Next we calculated the probability of winning the lottery. Dawson told us that the lottery is sometimes called the 'Tax on people who cannot do math." And we calculated why. We started with a "friendly" lottery. The numbers are 1-44, and a $1 ticket gives you two sets of six numbers. In this scenario, there are two favorable outcomes (either set of numbers), divided by the total outcomes (44 choose 6). This turned out to be 1/3,529,526. One in three million, and that's a friendly lottery!! Next, we calculated the odds of winning the PowerBall lottery. It turned out to be 1 in 175,223,510. Then we calculated how much you would have to win to recovery your "investment." Since PowerBall tickets are $2, you would have to win $350 million to break even. This does not include the government's 39% tax, your state income tax, or sharing the money with your family. We estimated that for the lottery to be a logical gamble, the jackpot would have to be $700 million, not accounting for having to share the winnings with others. It all boils down to this: The lottery, like any other gambling, does not make sense economically.

After the lecture, it was time for lunch. Today's lunch was the best I have had so far at VSA. They had everything you needed to make you own fajitas: beef, chicken, refried beans, rice, lettuce, tomato, cheese, sour cream, and of course tortillas. I have not been here a week yet, so I don't know if they have a weekly menu. I hope they do, because the fajitas were awesome. I can't wait to have them again. I think they were better than the salmon and lasagna they serve on Mondays and Fridays.

After lunch, we did independent study for another 30 minutes. I took and passed my second quiz, and moved on to Section 3. I just finished a few problems, when he had us stop. Next we did our daily activity. This time we were grouped into four groups of three. I was in a group with Brenden and Alex. We had to calculate the probability of every poker hand, assuming you were just dealt five cards from the deck. This was pretty easy for us, so we finished much earlier than the rest of the groups. When we asked Dawson what to do now, he told us he put the three of us together on purpose, because he knew this would happen. He had us flip over our papers, and calculate the probability of the same hands if a double deck was used. This also added a couple new hands to the mix, including five of a kind, a flush with one pair of duplicate cards, and a flush with two pairs of duplicate cards. We did not get very far with this, as we only had about 10 minutes. After we finished the activity, and took a break before presentations, it dawned on me that since Dawson grouped the three of us together, that means he considers me one of the top three students in the class! This really surprised me, as I did not think I stacked up that well among the seven Calculus students (including Alex and Brenden).

Next came presentations on our mathematicians. To be quite honest, I did not learn much from other people's presentations. About half of them just read off their slides. A couple people read whole paragraphs from their slides. You could tell these were copied, as they did not understand it at all, and couldn't even read it correctly. There were only five presentations that I learned something from, not including mine. Dawson randomly drew our cards to determine the order. I ended up going 8th. I gave my presentation, and everyone was impressed. One of the girls in the class even said, "Wow. You're a really good presenter." Dawson seconded that by saying, "That's the first thing I wrote in my notes. Excellent job." Again, I was amazed by this. I know I have lots of practice with public speaking, but I did not think I would impress anybody with it. Part of the reason it went well was that I stuck with concepts I could explain. Other people (who copied and pasted) did not understand what was on their slide, so they struggled with it. I was also immediately after three not-so-great presentations, so that was probably part of it as well.

During our presentations, a thunderstorm started. We could tell it was very close, because of how loud it was. The curtains on the windows were drawn, so we never saw the lightning. Fortunately, by the time all our presentations were over, the rain had stopped, and the sun came out once more.

Today was the last day of this session of Arête. Each week, you get a different Arête class, and on Fridays, the classes present their work. So tomorrow we only meet for five minutes and then continue on to see the presentations by each class. Today I made a cube puzzle. There are eight cubes, with different colors on each side. There are also eight hinges in various places. It's kind of like a Rubik's cube, in that there is a series of moves required to solve it. Unfortunately, the teacher is keeping it until tomorrow for the presentation, so I couldn't take a picture of it. :-(

A couple hours after dinner, I went to the gym, but it was closed again. It turns out, the hours are 7 AM to 7 PM. I just missed it by about 10 minutes. Anyway, tomorrow is Friday, so I will go with the running group again. I'm trying to exercise everyday, but at this rate, it may just be Monday, Wednesday, Friday.

Overall, my day started and ended badly (locked out of the gym), but the middle of the day was awesome (I impressed Dawson twice)!

Tomorrow evening is the VSA dance. We'll see how it goes. You can read about it tomorrow...