We had several discussions about probability and before we delve deeper on this topic, let us reinforce our knowledge by familiarizing ourselves with the terminologies and notations used. This is in preparation to more discussions ahead. Aside from probability, we will also learn more about permutations, combinations, statistics and other related fields. The following are the common terms used in probability as well as the notations used in most textbooks.
If a coin is tossed, when the coin comes to rest, it can show a tail or a head, each of which is an outcome.
Each roll of a die or toss of a coin is a trial.
An experiment consists of one or more trials. » Read more
This is the third part of the Experimental and Theoretical Probability Series.
In the second part of this series, we have observed in three different experiments that if two dice are rolled, it seems that the probability of getting the sums are not equal. Not only that, we have seen several consistent patterns; for example, 2 and 12 got the least number of rolls; while, 6,7, and 8 got the most.
To investigate this observation, we examine how to get a sum of 2, 12, and 6 first when we roll two dice, and then investigate other sums later. Recall that in the first part of this series, we experimented with two dice, one colored blue and the other red. To distinguish which number belongs to which dice, we color the numbers blue and red to denote blue and red dice. » Read more
In the Milk, Beads and Pascal’s Triangle article, we have talked about the Sister’s Dilemma, and how they toss coins and later roll dice to solve their problem. In this post, we are going to talk more about tossing coins and how they are connected to other mathematical topics.
The Interrupted Game
In a chess tournament in your school, two of your classmates, Sherwin and Carlo, made it to the championship game. The championship game was a race to 6. The score was 5-3, in favor of Sherwin.
Suppose, Carlo got sick, and the school agreed to divide the prize money worth $500 based on the players’ chance of winning the championship, how should the money be divided fairly? » Read more