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Maths Formulas

Probability Formula

We all are knowing about occurrences of various events and their chances to occur. Probability is a wonderfully usable and applicable field of mathematics. The theory of probability began in the 17th century in France by two mathematicians Blaise Pascal and Pierre de Fermat. In this article, we will mainly be focusing on probability formula and examples. Let us get started!

Probability Formula

What is Probability?

We are usually about a weather forecast at the end of a news bulletin on TV or we read about the weather conditions of our city for the next few days in the newspaper. They specifically use the term which is the probability.

Probability is the term used in math as well as in statistics very frequently. It is defined as the measure of chances for the occurrence of some event. It also provides the estimation of uncertainty of any event. For example, getting head or tail during toss of a coin is having a chance of \(\frac{1}{2}\) for both.

There are some terms used in the study of probability are as follows:

  1. Experiment: It is any phenomenon like rolling a dice, tossing a coin, drawing a card from a well-shuffled deck, etc.
  2. Outcome: It is the result of any event such as number appearing on a dice, side of a coin etc.
  3. Sample Space: It is the set of all possible outcomes.
  4. Event: It is the combination of possible outcomes or the subset of sample space. For example getting an even number on rolled dice, getting a head or tail on a flipped coin, taking out a king of any card suit.
  5. Probability Function: It is a function for giving the probability for each outcome.
  6. Odds in favor of the event: It is the ratio of the number of ways that an outcome can occur to the number of ways it cannot occur.
  7. Odds against the event: It is the ratio of the number of ways that an outcome cannot occur to the number of ways it can occur.

Probability Formulae

Probability = \( \frac{Number of a Favourable  outcome}{Total number of outcomes} \)

i.e.      P= \( \frac{N(E)}{N(S)} \) 


P probability
E event
S sample space.
n( E) the count of favourable outcomes


the size of the sample space.

P is the probability, E is some event and S is its sample space.

Where, n( E) = the count of favorable outcomes

and n(S) = the size of the sample space.

Solved Examples

To understand the above formula let us have some examples.

Q: Probability for getting an even number on the front face of a rolling dice.

Solution: Here sample space (S) = {1, 2, 3, 4, 5, 6} i.e. all possible outcomes.

And, event (E) = {2, 4, 6} i.e. even number occurrence.

Thus n (S) = 6 and n (E) = 3

Using this in the probability formula, we get:

P = \(\frac{3}{6}\) = \(\frac{1}{2}\) = 0.5

Therefore the chances of getting an even number upon rolling a dice is 0.5

Q: Find the probability of getting HEAD at least once on tossing a coin twice.

Solution: Here sample space (S) = {HH, HT, TH, TT}

H denotes Head and T denotes Tail.

So, favourable event (E) = {HH, HT, TH}

Thus n (S) = 4 and n (E) = 3

Using these values in probability formula, we get:

P = \(\frac{3}{4}\) = 0.75

Hence, the chances of getting at least one HEAD on tossing a coin twice are 0.75

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