Question

For the statement below: What is the misconception? How do you fix it?

A pitch in baseball can be called a ball or a strike or can be hit by the batter. As there are 3 possible outcomes, the probability of each is 1/3.

Answer 1

Generally when it is said that there are 3 possible outcomes, a person who is not well versed with the concept of probability can assume that each event will have same chance to occur and hence the probability of occurrence is 1/3. But this is a misconception because all the three events are not equally likely to occur. The probability of each of the event will be 1/3 only if a ball, strike or hit is equally likely to occur. In actual scenario, the probability of a hit can be much different from the probability of a ball or strike.

This can be fixed by referring to the records of baseball matches or by observing ongoing baseball matches and counting the number of hits, balls and strikes. It can be observed that, by the end of the game or in the records of baseball, there is considerable difference in the proportion of hits, balls and strikes. For example hit probability of players can vary from 5% to 50% or even more, depending on the player, pitcher and the match conditions. So, we cannot assume that the probability is same for each of the events.