Day 12: Discrete Probability

hello frndz,

Today we will learn about Discrete Probability!!

:- Discrete probability is an experiments that have a finite number of outcomes.
For eg. Rolling a device numbered 1 to 6 has 6 possible to outcomes: 1,2,3,4,5,6


:- D.P of an event is an experiment that has number of outcomes for event E out of all possible outcomes.
For eg. Rolling a device with getting odd number on face. Here Odd number on face is an event E.
Number of outcomes for event E = {1,3,5} = 3
Total possible outcomes = 6
Discrete probability = 3/6 = 1/2

(general Formula: P(E) = The number of outcomes in E / The total number of possible outcomes)


:- P(E) is a number between 0 and 1. If P(E) = 0, Event E is not possible and If P(E) = 1, then Event E is certain.

For eg. Probability of getting an odd number divisible by 2 is 0. (Not possible)
Another; probability of getting an even number divisible by 2 is 1. (Always)


:- "Not E" is the set of outcomes that are not outcomes in E.
For eg. In previous eg. of rolling device, getting even number on face = 1 - getting odd number of face


:- "E or F" is the set of outcomes in E or F or both.
"E and F" is the set of outcomes in both E and F.

For eg. In previous example of rolling device, getting an odd number(E) or prime number(F),
P(E or F) = P(E) + P(F) - P(E and F)
P(E and F) = {3,5}/6 = 2/6 = 1/3
P(E) = 1/2; P(F) = {1,3,5}/6 = 3/6 = 1/2

So P(E or F)  = 1/2 + 1/2 - 1/3 = 2/3



:- If E and F are independent events and occurrence of either event does not affect the probability that the other event occurs, then P(E and F) = P(E)P(F)
For eg. Rolling a device with getting even number(E) and Rolling another device with {5,6}(F) are independent events.
P(E) = 1/2
P(F) = {5,6}/6 = 1/2
So P(E and F) = 1/2*1/2  = 1/4
In this Case, P(E or F) = P(E) + P(F) - P(E)P(F)


:- If E and F are mutually exclusive events and "E and F" is not possible, then P(E and F) = 0
For eg. Rolling a device and flipping a coin are mutually exclusive events.
In this Case, P(E or F) = P(E) + P(F)



Okie guys, Keep practice On!! This is the end of Arithmetic.. From tomorrow on wards, we will go for Algebra..


Er. Ankur Garg
garg.ankur6@gmail.com