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# Different Probability Formulas

Probability formula with addition rule: Whenever an event is the union of two other events, say A and B, then
P(A or B) = P(A) + P(B) – P(A∩B)
P(A ∪ B) = P(A) + P(B) – P(A∩B)

Probability formula with the complementary rule: Whenever an event is the complement of another event, specifically, if A is an event, then P(not A) = 1 – P(A) or P(A’) = 1 – P(A).
P(A) + P(A′) = 1.

Probability formula with the conditional rule: When event A is already known to have occurred and the probability of event B is desired, then P(B, given A) = P(A and B), P(A, given B). It can be vice versa in the case of event B.
P(B∣A) = P(A∩B)/P(A)

Probability formula with multiplication rule: Whenever an event is the intersection of two other events, that is, events A and B need to occur simultaneously. Then P(A and B) = P(A)⋅P(B).
P(A∩B) = P(A)⋅P(B∣A)

Example 1: Find the probability of getting a number less than 5 when a dice is rolled by using the probability formula.

Solution

To find:
Probability of getting a number less than 5
Given: Sample space = {1,2,3,4,5,6}
Getting a number less than 5 = {1,2,3,4}
Therefore, n(S) = 6
n(A) = 4
Using Probability Formula,
P(A) = (n(A))/(n(s))
p(A) = 4/6
m = 2/3

Answer: The probability of getting a number less than 5 is 2/3.

Example 2: What is the probability of getting a sum of 9 when two dice are thrown?

Solution:

There is a total of 36 possibilities when we throw two dice.
To get the desired outcome i.e., 9, we can have the following favorable outcomes.
(4,5),(5,4),(6,3)(3,6). There are 4 favorable outcomes.
Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes in a sample space)
Probability of getting number 9 = 4 ÷ 36 = 1/9

Answer: Therefore the probability of getting a sum of 9 is 1/9.