The Bus Route Problem

For this blog I chose to write about the bus far problem. I like this problem because many people get it wrong just by guessing. It seems so simple and obvious as to what the answer is and many people are surprised to find that they are wrong. Just to test this, I showed both of my parents this problem. Not surprisingly, they both answered wrong after thinking about the problem for a few short seconds. As I explained it to them, I felt my understanding of the problem and what makes it so interesting grow. What the problem does is that it measures two separate things. As the diagram shows, you have a far greater chance (over half) of showing up to the station during the 35 minute interval. So to many  people, especially those waiting for a bus, it would seem that the average time for the bus to arrive was between 20 and 30 minutes. But this is not what the question is asking. If you average all the times on the diagram out, it comes to a perfect 15 minute interval between buses. So in fact, this bus service is indeed doing their job and buses are arrival at 15 minutes on average. My parents got quite the kick out of this one :)

Probability in Baseball

After reading Ms. Mariner's latest prompt about probability, I began thinking in my own life of situations where I use probability to help me. My immediate thought was baseball.

When I play baseball I am always trying to get the upper hand on my opponent. We just began our season this past Tuesday playing the Belen Eagles. One of the ways I can gain an advantage is analyzing pitch sequences and being able to guess on what pitch the pitcher is going to throw in any given situation. 

The pitcher we faced on Tuesday threw 3 pitches. A fastball, change-up, and a curve ball. By the end of the second inning, I had made a mental note of how often he was throwing each pitch and in what kind of situation he was throwing it in. He threw his fastball 60% of the time,  his change-up 10% of the time and his curve ball that 30% of the time. When I go up to the plate to hit, I begin to think what pitch I am most likely to see. If I consider his pitch usage, I know that there is a 3/5 chance of me getting a fastball and because of this knowledge I am able to sit and wait on the fastball so I can crush it. This brings me to consider what the probability is of him throwing me two straight fastballs. (3/5)(3/5) = 36% chance of a fastball. These probabilities can be found out for all of his pitches in any given situation. 

Another thing I have to consider that is not measurable is how he pitches certain players. While my fractions are very helpful, that is not the only thing to consider. Say in my first at bat I hit a double to the wall on a first pitch fastball. My next at bat the pitcher will remember this and try to not throw me the same pitch. This means that the probability of a fastball decreases and the probability of a curve ball or change-up decreases. 

I could write on this topic for quite a long time but I want to keep this one a bit shorter. (Don't want to  waste any of your time :) )