## How to Calculate and Solve for Dependent Events | Probability

The image above represents dependent events.

To compute for dependent events, four essential parameters are needed and these parameters are Number of Times Event A can occur (xA), Number of Times Event B can occur (xB) and Total Number of All Possible Outcomes (N).

The formula for calculating independent events:

P(A and B) = P(A) x P(B|A)

Where;

P(A and B) = Dependent events
xA = Number of Times Event A can occur
xB = Number of Times Event B can occur
N = Total Number of All Possible Outcomes
P(A) = xAN
P(B|A) = xB(N – 1)

Let’s solve an example;
Find the dependent events when the number of times event A can occur is 8, number of times event B can occur is 11 and the total number of all possible outcomes is 18.

This implies that;

xA = Number of Times Event A can occur = 8
xB = Number of Times Event B can occur = 11
N = Total Number of All Possible Outcomes = 18

P(A and B) = P(A) x P(B|A)
P(A and B) = xAN x xB(N – 1)
P(A and B) = 818 x 1117
P(A and B) = (8)(11)(18)(17)
P(A and B) = 88306
Dividing the numerator and denominator by 2
P(A and B) = 44153
P(A and B) = 0.287

Therefore, the dependent events is 0.287.

## How to Calculate and Solve for Independent Events | Probability

The image above represents independent events.

To compute for independent events, four essential parameters are needed and these parameters are Number of Times Event A can occur (xA), Number of Times Event B can occur (xB) and Total Number of All Possible Outcomes (N).

The formula for calculating independent events:

P(A and B) = P(A) x P(B)

Where;

P(A and B) = Independent events
xA = Number of Times Event A can occur
xB = Number of Times Event B can occur
N = Total Number of All Possible Outcomes
P(A) = xAN
P(B) = xBN

Let’s solve an example;
Find the independent events when the number of times event A can occur is 11, number of times event B can occur is 15 and the total number of all possible outcomes is 22.

This implies that;

xA = Number of Times Event A can occur = 11
xB = Number of Times Event B can occur = 15
N = Total Number of All Possible Outcomes = 22

P(A and B) = P(A) x P(B)
P(A and B) = xAN x xBN
P(A and B) = 1122 x 1522
P(A and B) = (11)(15)(22)(22)
P(A and B) = 165484
Dividing the numerator and denominator by 11
P(A and B) = 1544
P(A and B) = 0.3409

Therefore, the independent events is 0.3409.

## How to Calculate and Solve for Impossibility | Probability

The image above represents impossibility.

To compute for impossibility, one essential parameter is needed and this parameter is Total Number of All Possible Outcomes (N).

The formula for calculating impossibility:

P(A) = x N

Where;

P(A) = Imposssibility
N = Total Number of All Possible Outcomes

Let’s solve an example;
Find the impossibility when the total number of all possible outcomes is 12.

This implies that;

N = Total Number of All Possible Outcomes = 12

P(A) = x N
P(A) = 0 12
P(A) = 0

Therefore, P(impossibility) is 0.

## How to Calculate and Solve for P(not A) | Probability

The image above represents P(not A).

To compute for P(not A), two essential parameters are needed and these parameters are Number of Times in Which Event A Can Occur (x) and Total Number of All Possible Outcomes (N).

The formula for calculating P(not A):

P(not A) = (N – x)N

Where;

x = Number of Times in Which Event A can Occur
N = Total Number of All Possible Outcomes

Let’s solve an example;
Find the P(not A) when the number of times in which event A can occur is 7 and the total number of all possible outcomes is 11.

This implies that;

x = Number of Times in Which Event A can Occur = 7
N = Total Number of All Possible Outcomes = 11

P(not A) = (N – x) N
P(not A) = (11 – 7) 11
P(not A) = 4 11
P(not A) = 0.36

Therefore, the P(not A) is 0.36.

## How to Calculate and Solve for P(A) | Probability

The image above represents P(A).

To compute for P(A), two essential parameters are needed and these parameters are Number of Times in Which Event A Can Occur (x) and Total Number of All Possible Outcomes (N).

The formula for calculating P(A):

P(A) = x N

Where;

x = Number of Times in Which Event A can Occur
N = Total Number of All Possible Outcomes

Let’s solve an example;
Find the P(A) when the number of times in which event A can occur is 10 and the total number of all possible outcomes is 22.

This implies that;

x = Number of Times in Which Event A can Occur = 10
N = Total Number of All Possible Outcomes = 22

P(A) = x N
P(A) = 10 22
Dividing the numerator and denominator by 2
P(A) = 5 11
P(A) = 0.45

Therefore, the P(A) is 0.45.

## How to Calculate and Solve for Certainty | Probability

The image above represents Certainty.

To compute for certainty, one essential parameter is needed and this parameter is Total Number of All Possible Outcomes (N).

The formula for calculating Certainty:

P(A) = x N = N N

Where;

P(A) = Certainty
N = Total Number of All Possible Outcomes = 2

Let’s solve an example;
Given that the total number of all possible outcomes is 2. Find the Certainty?

This implies that;

N = Total Number of All Possible Outcomes = 2

P(A) = x N = N N
P(A) = 2 2
P(A) = 1

Therefore, P(certainty) is 1.