Applied Probability

Introduction of applied probability:

Analysis of random situation, condition, or events is called Probability. Probability is the numerical analysis of impossibility to absolute certainty. Probability is the possibility that something will happen - how likely it is that some event will happen. For example, when picking a one card of diamond from the pack of 52 cards, the probability of picking a diamond card is 13/52, or 1/4.


Formulas for applied probability


Formula 1: Compliment

If AA and A'A' are complements then P(A) + P(A' ) = 1P(A)+P(A' )=1

Formula 2: Addition Rule

P(A OR B) = P(A) + P(B) - P(A AND B)P(A OR B)=P(A)+P(B)-P(A AND B)

Formula 3: Mutually Exclusive

If AA and BB are mutually exclusive then

P(A AND B) = 0P(A AND B)=0 ; so

P(A OR B) = P(A) + P(B)P(A OR B)=P(A)+P(B).

Formula 4: Multiplication Rule

P(A AND B) = P(B) P(A|B)P(A AND B)=P(B)P(A|B)

P(A AND B) = P(A) P(B|A)P(A AND B)=P(A)P(B|A)

Formula 5: Independence

If AA and BB are independent then:

P(A|B) = P(A)P(A|B)=P(A)

P(B|A)= P(B)P(B|A) =P(B)

P(A AND B) = P(A) P(B)

Understanding Partial Fraction Method is always challenging for me but thanks to all math help websites to help me out.

Examples for applied probability:


Applied Probability Problem 1: A die is rolled, find the probability that an odd number is obtained.

Solution:

Let us first write the sample space S.

S = {1,2,3,4,5,6}
Let E be the event "an odd number is obtained" and write it down.

E = {1,3,5}
We now use the formula of the classical probability.

P(E) = n(E) / n(S) = 3 / 6 = 1 / 2
Applied Probability Problem 2: Two coins are tossed, find the probability that two tails are obtained.

Solution 2:

The sample space S is given by.

S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two tails are obtained".

E = {(T,T)}
We use the formula of the classical probability.

P(E) = n(E) / n(S) = 1 / 4