The normal distribution is also called as Gaussian Distribution. The normal distribution was first discovered by De-Moivre (1667 "' 1754) in 1733 as a limiting case of Binomial distribution. It was also known to Laplace not later than 1744 but through a historical error it has been credited to Gauss who first made reference to it in 1809.

The probability is the sketch of match up information or format that an incidence will happen. The probability of an event C should be represented as P(C). The probability value is forever among 0 and 1. In probability we are having few numbers of formulas. In this article, we will see preparation of probability formulas, examples and exam questions.

Formulas in Preparation for Probability

Formula 1: Compliment

If A and A' are compliments, then P(A) + P(A') = 1

Formula 2: Addition Rule

P(A or B) = P(A) + P(B) "" P(A and B)

Formula 3: Mutually exclusive events.

If A as well as B are mutually exclusive events, after that P(A and B) = 0

Therefore, 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(A)P(B|A)

Formula 5: Independence events.

If A and B are independent events then,

P(A|B) = P(A)

P(B|A) = P(B)

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

These are the preparation of formulas in probability.

Example Problems Preparation for Probability

Example 1:

What is the probability of getting sum of 6 or 8, when the two dice are rolled?

Solution:

When the two dice is rolled, the sample space is, n(S) = 36

In this problem, we want to use addition rule of probability.

Let A be the event of getting sum as 6.

So, n(A) = {(1,5), (2,4), (3,3), (4,2), (5,1)}

Let B be the event of getting sum as 8.

So, n(B) = {(2,6), (3,5), (4,4), (5,3), (6,2)}

So, n(A) = 5 and n(B) = 5

That means, P(A) = 5/36 and P(B) = 5/36

Here, P(A and B) = 0

Therefore, P(A or B) = P(A) + P(B) "" P(A and B)

= 5/36 + 5/36 "" 0

= 10/36

= 5/18

Example 2:

The two dice are rolled. Find the probability of getting 3 on first dice and even number of second dice?

Solution:

There are two independent events are happening.

So, here n(S) = 6

Let, A be the event of getting number "3", P(A) = 1/6

Let, B be the event of getting even number, P(B) = 3/6

Therefore, P(A and B) = P(A) P(B)

= (1/6) (3/6)

= 3/36

= 1/12

Preparation for Exam Questions Probability

1. What is the addition rule of the events M and N?

2. What is the probability of getting sum of 5 or 7, when the two dice are rolled?

3. The two dice could be rolled. Find the probability of getting 2 on first dice and odd number of second dice?

Answers:

1. P(M or N) = P(M) + P(N) "" P(M and N)

2. 5/18

3. 1/12

That"s all about preparation for probability formulas exam.