Probability and Expected Values

A Family Planning Strategy:
By starting this example with the sentence “have children until you have a girl” the author gives like an introduction of what he is about to explain. In this example Nob Heckard gives an introduction of what the expected value is. He explains expected value as “the theoretical mean for a large sample or many repeats of a process”. Therefore, this is how we understand that expected value is the probability of things happening in the long term. In the example Bob shows that there is a 50% chance for the baby to be a girl, and the other 50% to be a boy. After some calculations he found that Expected value could be found by adding the multiplication of the “value and probability” of all the things we are trying to combine. By doing this you can find that the sex mix of boys-girls stays equal.

Swedish Parking Example:
Rather than having meters the policemen look at the air valve’s position on two of the car wheels. If the valves to not move after the hours (the maximum parking time) then the car is ticketed. However, some car owners would argue that they moved the car, parked in the same place, and the valves happened to end up in the same position as before. The multiplication rule must be used to find the probability of this, since the problem is conditional. If the person takes two of the car wheels and compares the valves position to a clock (having 12 likely positions) then one could assume p(1/12)x p(1/12) = 1/144. The one stands for the likelihood of the valve being in the one position it was in before and the 12 stands for the 12 different positions possible. A person’s probability to park their car in the same way is 1/144.

A Roulette Wheel:
First, one must realize that there are 38 numbers total. Take for example that the probability of winning $35 is 1/38. The probability of losing $1 would then be 37/38. In order to calculate the expected value, however, one must incorporate the total value to come to the accurate value. The chance of winning $35 times the actual probability subtracted from the chance of losing $1 is equal to $0.05. Considering the long term effects, neither side truly gains anything. Thus making roulette an unfair game.