Solving Probability Problems Using The Markov Chains

Probability is everywhere, but it is more likely the science of uncertainty. When there is no way or a mathematical doubt, probability is used. Many mathematical evaluations and even gaming outcomes are dependent on math probability. There can be a probability of a person winning or losing the game by 30% or more. Players can head to , and play the games according to the probability they feel. Probability helps people decide how a particular situation will turn up.

A Probability Space is used in math that helps get the possible outcomes. The sample space here can have an infinite set. There can be an infinite number of possibilities made with the help of this magical math term. But, there can be a few problems occurring with this math term to use the Markov Chains. A.A. Markov devised it, and this probability chain is the example of Stochastic Processes or the random variable that will evolve. The Markov Chains is a random process that bounces between the different states.

Solve Problems Using Markov Chains

Math is one of the complicated subjects for many people, but the probability makes it easier to carry out the results if there are many problems. A few problems may be calculation intensive, but you can sort out others with the Markov Chains. It helps raise the matrix to a specific power, and then the user needs to find the inverse of the matrix. This concept helps organize the probability and find the solutions to the problems.

A few problems discussed under Markov Chains include the classic problems in probability like rolling dice, tossing coins, coupon collector problem, and occupancy problem. The problems listed here provide an insight into the Stochastic Processes. Here are a few of them:

  1. Problem-1: The fair coins are tossed until the appearance of the four consecutive heads. Here, the user needs to determine the mean number of tosses required.
  2. Problem-2: The Markov Fleas are the hopping fleas that hop around the vertices of the transition diagram drawn in the shape of two triangles. So, he named his fleas the Glee Flea, Forget Flea, Skill Flea, and Purpose Flea.
  3. Problem-3: The fair dice are thrown by the user and rolled until each face has appeared once. Here, the expected number of dice rolls needs to be achieved.
  4. Problem-4: Coming onto the fair coin-tossing until the appearance of the 4 consecutive heads. Here, the probability appears like the user makes the nine dancing flips to get the four consecutive heads or almost nine flips must be made to get the 4 consecutive heads.
  5. Problem-5: Here, we will talk about the Stochastic Processes. In the Gambler’s Ruin section, the X represents the amount spent and Xt, and the ‘T’ is the toss. Now, it can be represented through the transition diagram and find the probability of the amount of money spent by the gambler.
  6. Problem-6: One ball at a time is thrown into the six different cells. So, how many balls need to be thrown to occupy all 6 cells?
  7. Problem-7: Now, taking the above example of throwing the balls into 6 cells where one ball is thrown, the number of balls is stated. Here, 8 balls are thrown in these cells. The probability taken is ‘k’ for the balls being thrown into these 6 cells to occupy them all.

    Wrapping Up

    Everything has a certain probability assigned to it. It can be an outcome while playing the game or throwing the dice. The Marko Chains makes the reading of the problems a little easier.