Real life example of probability
Probability is the branch of mathematics that deals with calculating the numeric value of a chance that an event may occur. In our daya to day conversations, we do often talk about how many chances that it will rain today. The chance of raining can be a very heavy rain or light rain or even no rain at all. We can only make a guess by seeing the clouds in the sky or by recalling the past year that if it rained on the same day of the last year. Or if we can recall back upto more years in the past that if it rained on the same day as of today, that will make our guess more right to say that how many chances there are to rain today.
If it has been raining for the last few years on the same day also then our guess will be more towards yes
it will rain today also. If it went some dry days also for the last few years other than receiving raining
then our guess will be less affirmed that it will rain today.
This guessing of rain or finding out the change of rain in our day to day conversations is the
same probability of mathematics that serves the same objective of finding out the chances in numbers that it
will rain today or not.
Probability in maths calculates the chance of happening an event, for example the guessing of rain, using
formulas and makes a guess in numbers that the chances to rain are 10% or 50% or 90% etc.
Terms used in probability
To understand probability there are some terms those are used very often like events, sample space, favourable outcomes and possible outcomes.
Experiment
Finding the chance or probability of raining on a day is an experiment. So, experiment is a complete procedure of calculating the probability of a problem.
Example 1: To find the probability of getting number 3 after rolling a dice.
Example 2: To find the probability of getting a head when a coin is tossed.
Outcome
Outcome in probability is a unique result obtained while conducting an experiment. An experiment may consist of one or more than one outcome.
Example 1: When a dice is rolled, only six unique outcomes are possible, i.e. 1, 2, 3, 4, 5 and 6. At one time a rolled dice can show only one of the numbers out of six possible numbers.
Example 2: When a coin is tossed, it can result in only two unique outcomes, which are head and tail. A tossed coin, only a head or a tail can be seen at one time.
Sample space
Sample space in probability is set of all possible outcomes that can be resulted out of an experiment.
Example 1: The set of six outcomes resulted from a rolled dice makes a sample space of six numbers, which is {1, 2, 3, 4, 5, 6}.
Example 2: A tossed coin has two outcomes only which are head (H) and tail (T). So its sample space can be written as {H, T}.
Event
When an experiment conducted, it consists of multiple events that are processed. The outcomes obtained from each event will match the outcomes of the sample space of the experiment.
Example 1: In an experiment of getting an even number whn a dice rolled, the event consists of three outcomes. {2,4,6}.
Example 2: The event in an experiment of getting a head can be {H}.
Mutually exclusive events
The two events can be said as mutually exclusive events if all of their outcomes are unique, not matching. In other words, the two events cannot happen at the same time.
Example 1: The number that show up in rolling a dice are mutually exclusively events because the two numbers cannot show up in a single event.
Example 2: Tossing a coin can turn up either a head or tail at one time. Both head and tail can not turn up at the same time.
How to calculate probability
The numerical value of probability can only lie between 0 and 1. An event with the value of probability equal
to 0 means the event is not possible to occur or has not occurred. If its value is 1 then the event has
occurred for sure or is certain to occur.
Probability of an event can be calculated mathematically by dividing the number of favourable outcomes by
the total number of possible outcomes or the total number of outcomes in the sample space.
P(E) = Number of favourable outcomesTotal number of possible
outcomes
Here, P(E) is the probability of an event E. The value of P(E) can lie only between 0 and 1, such that
0 ≤ P(E) ≤ 1
Example 1: What is the probability of getting the number 2 when a dice is tossed once?
In an event of tossing a dice, there are maximum possible six numbers viz: 1, 2, 3, 4,
5, and 6 those can appear after the dice is landed. Therefore, the sample space is {1, 2, 3, 4, 5, 6} or in other words
these are the total number of possible outcomes.
∴ Total number of possible outcomes = 6
As dice is tossed once, therefore there is only one chance when 2 can appear.
∴ Number of favourable outcomes = 1
P(E) = Number of favourable outcomesTotal number of possible
outcomes
= 16
Example 2: What is the probability of getting head when a coin is tossed once?
There are two possible outcomes head (H) and tail (T) that can show up when a coin is tossed.
Therefore, the sample space is {H, T}.
∴ Total number of possible outcomes = 2
When coin is tossed once, there is only once time, we can get a head.
∴ Number of favourable outcomes = 1
P(E) = 12
