Probability Formulas

The likelihood of an event happening is probability. When a random experiment is entertained, one of the first questions that come in our mind is: What is the probability that a certain event occurs?  A probability is a chance of prediction. When we assume that, let’s say, x be the chances of happening an event then at the same time (1-x) are the chances for “not happening” of an event.

Similarly, if the probability of an event occurring is “a” and an independent probability is “b”, then the probability of both the event occurring is “ab”. We can use the formula to find the chances of happening of an event.

The formula of probability of an event is:

Probability of an event

Here, favourable outcome we mean that the outcome of interest.

Sometimes students get confused about the word “favourable outcome” with “desirable outcome”. In some of the requirements, losing in a certain test or occurrence of an undesirable outcome can be a favourable event for the experiments run.

Basic Probability Formulas

Let A and B are two events. The probability formula are listed as below:

Probability Range 0 ≤ P(A) ≤ 1
Rule of Addition P(A∪B) = P(A) + P(B) – P(A∩B)
Rule of Complementary Events P(A’) + P(A) = 1
Disjoint Events P(A∩B) = 0
Independent Events P(A∩B) = P(A) ⋅ P(B)
Conditional Probability P(A | B) = P(A∩B) / P(B)
Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)

Probability Formulas Examples

Example 1: What is the probability that a card taken from a standard deck, is an Ace?


Total number of cards a standard pack contains = 52

A deck of cards contain Ace = 4 cards

So, the number of favourable outcome = 4

Now, by looking at the formula,

Probability of finding an ace from a deck is,

P(Ace) = (Number of favourable outcome) / (Total number of favourable outcomes)

P(Ace) = 4/52

= 1/13

So we can say that the probability of getting an ace is 1/13.

Example 2: Calculate the probability of getting an odd number if a dice is rolled?

Solution: Sample space (S) = {1, 2, 3, 4, 5, 6}

Let “E” be the event of getting an odd number, E = {1, 3, 5}

So, the Probability of getting an odd number P(E) = (Number of outcomes favorable)/(Total number of outcomes) = n(E)/n(S) = 3/6 = ½

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Practise This Question

Which of the following can conduct electricity?