06 Feb Introduction to Probability
At Miracle Learning Centre, we teach you interesting stuff in math tuition. In this math tuition, we are going to talk about probability. Probability is an extremely elegant branch of mathematics. Probability, as the name suggests, is about calculating the chance of a particular event happening. An thorough understanding of probability is required to understand a lot of topics in math, especially related to statistics and in this math tuition, we are going to learn about the basics of probability.
As mentioned above, probability deals with chance. In other words, probability quantifies the likelihood of an event. So what is probability? Let us see with an example.
Consider that we are to tossing a coin. If we were asked about the chance that it will turn out to be heads, we could calculate it fairly simply. In a coin toss, there are only two possibilities: either it turns out to be “heads” or “tails”. As a result, the chance that it will be “heads” is 1 in 2 which is 50%. Similarly, for “tails” as well, the chance is exactly 50%. In this case, the event that we are talking about is the outcome of a coin flip. As we calculated, the chance that it turns out to be heads is ½ or 50%. This chance is known as the probability. In other words, we could also say that the probability that the outcome of the coin flip will be heads is around ½ or 50%.
Let us take another example. In this case, we are going to consider a simple scenario. Let’s say you are at a bus stop and you see there are four empty seats marked A, B, C and D. Now you are asked to calculate the probability of you sitting on the seat C. Let us see how we can calculate this. In this case, the total number of possibilities is 4 i.e. you either sit on seat A or B or C or D. The number of scenarios for which you go on to sit on C is 1. As a result, the probability is ¼ or 25%.
In fact, the probability of any event, say E, is calculated using the following formula:
Probability of event E = P(E) = (Number of possible occurrences of event E)/(Number of occurrences of all possible scenarios)
It is important to mention here the fact that probability of any event is always less than or equal to 1. Also, probability cannot be negative.
If probability of an event is 1, then the event occurs always. For example, if you have a coin with both sides marked as “heads”, the probability that you will get “heads” is 1. On the other hand, for such an “unfair” coin, the probability of getting “tails” is 0 and if the probability is 0 for any event, then the event can never occur.
Mutually Exclusive Events and Probability
This is an extremely important to understand probability and this section of this math tuition, we are going to discuss about such events. So, what are mutually exclusive events? Two events, say event A and event B are said to be mutually exclusive when both of them cannot occur simultaneously. For example, when we flip a coin, we cannot get both “heads” as well “tails” as the outcome – it has to be either “heads” or “tails”.
If two events A and B are mutually exclusive, then the probability of either A or B happening can be worked out by using the following formula:
P (A or B) = P(A) + P(B)
Independent events and Probability
Another category of events in the context of probability is independent events. Two events are independent if the occurrence of one does not affect the other event in any way. Let us see this with an example.
In this scenario, there is a box in which 4 black and 3 red balls are there. If you are told to pick two balls at random, what is the probability that you will pick a black ball and a red ball?
At first, there are 4 black balls so total number of possibilities of picking up a black ball is 4. On the other hand, in total there are 7 balls.
On the second time however, there will be a ball less and the total number of balls will become 6. As a result, the event of picking a ball first time is affecting the event of picking a ball for the second time. Clearly, these events in this case are not independent.
On the other hand, let us take a scenario where you are flipping a coin and at the same time, rolling a dice. In this case, the two events are independent and the occurrence of one does not affect the same of the other event.
If two events A and B are independent, then the probability of A and B happening could be worked out using the following formula:
P (A and B) = P(A) * P(B)
It is not possible to cover the entire topic of probability in one article. In this math tuition, we have just gone through the basics of probability and hopefully this will help you to develop a basic understanding of the topic. In case you feel any difficulty in understanding any of the concepts discussed here, feel free to seek help from your peers or from your teachers at math tuitions. Look out for the next math tuition from Miracle Learning Centre.