Data Science different topic explanation -- Part-3 -- Event Types

[anish-arya]

This is Data Science different topic explanation conversation series.
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Part-1:

Data Science different explanation -- An introduction

Data Science different explanation – An introduction [image] There are a lot of engineers who have never been involved in the field of statistics or Data Science. But in order to build data pipelines or rewrite produced code by Data Scientists to an adequate, easily maintained code many nuances and misunderstandings arise on the engineering side. For those Data/ML engineers and novice Data Scientists, I’ve made this series of posts. I will try to explain some basic approaches in plain eng…

Part-2:

Data Science different topic explanation -- Part-2 -- Events. Probabilities of events

If you missed the previous post, here’s the below mentioned link. Data Science different topic explanation – Part-2 – Events. Probabilities of events One of the basic concepts in statistics in an event. Events are simply results of experiments. Events can be certain impossible, or random. A certain event is an event that as a result of an experiment (the execution of certain actions with a certain set of conditions) will occur in 100% cases. For instance, tossed coin will certainly fall (on…

Data Science different topic explanation – Part-3 – Event Types

Independent and Dependent events

Two random events A and B are called independent if the occurrence of one of them does not change the probability of the occurrence of the other. Otherwise, events A and B are called dependent.

Counterintuitively, knowing that the coin landed on the head on the first toss, does not provide any useful information for determining what the coin will land on the next toss. The probability of a head or a tail on the next toss is still 1/2, regardless of the outcome of the first toss.

Probabilities of independent events should be multiplied to get the total probability of the occurrence of all of them.

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[anish-arya]

Continue above post.

Example: What are the chances of getting heads 3 times in a row?

Let’s define possible outcomes of 3 coin tosses (H-Heads, T-tails):

HHH, HHT, HTH, THH, TTH HTH, HTT, TTT

Number of ways it can happen: 1

Total number of outcomes: 8

So, the answer is 1/8. However, we know that the results of a coin toss are independent and we can multiply them to get the total probability: P(3x heads) = P(heads)P(heads)P(heads) = 1/2 * 1/2 * 1/2 = 1/8

On the other hand, knowing that the first card drawn from a deck is an ace does provide useful information for calculating the probabilities of drawing yet another ace going to be 3 over 51, instead of 4 over 52 because we know that we already remove on of the aces from the deck. You can think about that in your next poker game.

Next post: Disjoint and overlapping events