Probability on one hand can be simple and that is more of the start but seems to be complicated as you dig deeper. The truth is, unless you get to know what needs to be done as you proceed, you’ll always be struggling to get problems solved. There are aspects that required simple application of some concepts which are not necessarily tricks. Unlike the fundamentals where you’ll be required to calculate for dice problems or that of coins, you can be made to tackle problems involving combinations and permutations.
Having started with probability here, taking a good look at the definition will help a lot. Probability happens to be a branch of Math which uses numbers to predict the outcome of events. This study depends largely on numbers throughout its concepts, so that is what your focus should be on: numbers. The basic idea every one must have is that, these numbers that are involved here falls within two numbers: one and zero. These two numbers are also included and so you should be expecting them as well.
Before a student or any other learner starts with probability, the interpretation of these two digit should be known. The number one (1) in probability indicates that a stated event will certainly happen. Again, zero (0) when mentioned here indicates that, the event under consideration cannot happen or it is simply impossible. From these basic understanding, you can interpret the outcomes for other values that falls within the range whenever you’re being given a problem.
Let’s continue digging: considering problems regarding rolling a fair die or tossing a fair coin. You can be asked to predict the chances for which a “four” can pop up, that is for a die. For a fair coin being tossed, you can be asked to find the chances of obtaining a tail. These are all problems that are likely to come your way as you deal with the basic probability concept. Now, let’s consider when a problem states that a fair die was rolled once, and that what should be the chances of “four” becoming the result.
First, you’ll always have the keyword “fair” in your question. What does that really mean here: does it cause a difference when omitted? That’s right: It really causes a change when omitted. In probability, more attention is given to each event to make sure accurate random outcome is produced. Though the result is always not certain, but there is the need to ensure that there is no bias during the occurrence of the event.
Tackling this basic question, you’ll need two data: the sample space, and the number of times at which the event occurred. The sample space here is a term used to describe the total possible outcome of the events. In this case, rolling a fair die will result in a sample space of six (6). Why? This is because, the possible outcome could be one, two, three, four, five, six: any one of them could pop up as the final result but not more than one.
Then, proceeding to find the number of times this final answer may pop up which is “four” for now, four can only be obtained once since this fair die was rolled once. For that reason, considering the probability of “four” popping up will be one out of six. That will run through when you decide to consider another digit aside a “four”. Actually, the concept here can be extended to questions involving tossing a coin. Let’s dig deeper this time: as you proceed with probability, you’ll come across two major terms: permutation and combination.
Permutation is more concerned about the number of times a certain group of items can be arranged. Talking of combination in probability, that deals with the selection of specific items from a particular group of items. Always, questions won’t state whether they demand combination ideas: the same applies to permutation. You’re expected to know the appropriate concept to go in for after the problem is given.
Questions similar to finding the number of arrangement that say, five people can sit on a bench that can take only five persons will require the idea of permutation. For combination, you may be asked to find the chances of picking say, three marbles from a group consisting of ten marbles. Determining the type of concept to use is part of the required answer: Permutation and combination are available on your calculators. For that reason, you wouldn’t have to stress yourself with their calculation having learnt some extra principles.