Probability refers to the chance or likelihood of a particular event taking place. It’s a numerical measure between 0 and 1 that expresses how probable an event is. The closer a probability is to 1, the more certain the event. Conversely, a probability closer to 0 indicates a less likely event.
An experiment is process that is performed to understand and observe possible outcomes. for example, rolling a dice is an experiment.
Set of all outcomes of an experiment is called the sample space. for example, while rolling a dice the event may be 1, 2, 3, 4, 5 or 6, in this case the set of number from 1 to 6 is the sample space as these are all the possible outcomes.
An outcome which same as the desired outcome is favorable outcome. for example, If getting a heads in a coin flip is desired outcome and the result of the flipping is also heads, it is a favorable outcome.
An event is an outcome of the experiment. for example, getting a number between 1 to 6 while rolling a dice is an event.
there are different types of events,
Mutually exclusive events are the events that cannot happens at the same time and exactly one of them must happen, these are also referred as complimentary events, for example, war and peace are mutually exclusive events they cannot happen at the same time.
Independent events are the events whose occurrence is not dependent on any other event, for example, while flipping a coin event of heads or tails are not dependent on each other. So, these events are independent events.
Dependent events are the events in an experiment that are affected by other event, for example, drawing a marble from a bag which has marbles 2 red and 3 green marbles. In first event when you drew 1 red marble now in the second event the probability of red or green marble is affected by the first event. Because now the size of sample space has changed.
The events are said to be equally likely if the chances of them occurring are same. We can understand this with coin flipping example, here the chances for a heads or tails are same, hence they are equally likely.
What are complimentary events?
In a series of events, if an event can only occur when other event did not occur. These dependent events are referred to as complimentary events.
When probability is being calculated for a single event, it is called simple event. for example, tossing a single coin.
When probability is being calculated for a more than one events at the same time, it is called compound event. for example, tossing more than one coin at a time.
The basic formula for calculating probability is:
P(E) = Favorable Outcomes / Total Possible Outcomes
where:
Imagine flipping a fair (unbiased) coin. There are two possible outcomes: heads or tails. Let’s calculate the probability of getting heads:
Therefore, the probability of getting heads (P(heads)) is:
P(heads) = 1 / 2 = 0.5
This means there’s a 50% chance of getting heads when flipping a fair coin.
P(E') = 1 - P(E)
P(A U B) = P(A) + P(B)
This rule applies to events which are mutually exclusive meaning they cannot occur together, these are also referred as disjoint, here the probability of either A or B happening is denoted by (A U B).
P(A U B) = P(A) + P(B) - P(A∩B)
When two events can occur together, or we can say when two events are overlapping, to avoid the overcounting outcomes we need to adjust the outcomes that fall into both categories. Here, P(A∩B) represents the probability of both A and B happening together (intersection of events)
P(A∩B) = P(A) * P(B)
When two events are independent of each other, what is the probability of combination of outcomes, for example, choosing a movie genre and snack. if you had to choose between comedy, drama and action and for snack you had to choose between popcorn and candy.
Event A: Picking a comedy movie (P(A) = 1/3, assuming you are equally likely to pick comedy, drama, or action)
Event B: Selecting popcorn as your snack (P(B) = 1/2, since you could choose popcorn or candy
What is the probability of selecting a comedy movie and popcorn? (P(A∩B))
Using the formula: P(A∩B) = P(A) * P(B) = (1/3) * (1/2) = 1/6
P(A|B)=P(A∩B)/P(B)
Let’s take the example of train being delayed due to rainy weather, given that it is raining (Event A), what is the probability of train being delayed or we can say how much does the rain increases the chance of training getting delayed?
Here is a table summarizing an example scenario, focusing on weather conditions that might cause delays:
| Weather Condition | Total Days with Condition | Delayed Trains on Those Days |
|---|---|---|
| Rain | 20 | 10 |
| Snowfall | 10 | 8 |
| Fog | 15 | 5 |
| Total | 45 | 23 |
What is the probability of train getting delayed due to any weather?
What is the probability of train getting delayed due to different weather conditions?
This analysis shows that chances of the train getting delayed are highest on rainy days
We hope you found the information helpful! If you learned something valuable, consider sharing it with your friends, family, and social networks.
Reference: Khan Acedemy
Hi, I am Vishal Jaiswal, I have about a decade of experience of working in MNCs like Genpact, Savista, Ingenious. Currently i am working in EXL as a senior quality analyst. Using my writing skills i want to share the experience i have gained and help as many as i can.
SQL Interview Question at Zomato: These questions were recently asked in interview at Zomato, you…
Introduction: SQL Indexing and Query Optimization SQL indexing is a critical concept that can drastically…
This article is about the SQL Interview Questions asked by Walmart for their Data Analyst…
You must be able to answer these SQL Interview Questions if you are applying for…
This article tackles common SQL Interview Questions asked by EY, offering detailed solutions and explanations…
1164. Product Price at a Given Date: Learn how to track and select price from…