In this article, you will learn how to find the Probability of an Event in a few simple steps.

## Step by step guide to Finding Probability of an Event

Probability is commonly used to describe the mind’s attitude toward propositions that we are not sure are true. The statements in question are usually in the form of “Does a particular event occur?” And our minds’ attitude to the form “How confident are we that this will happen?” Is. Our confidence level can be described numerically, which takes a value between \(0\) and \(1\) and we call it probability. The more likely an event is, the more confident we are that it will happen.

The probability of each event is the ratio of the number of a wanted outcome to the number of all possible outcomes:

\(The probability of an event=\frac{The number of a wanted outcome}{The number of a possible outcome}\)

Note: wanted outcomes are the outcomes that have been studied and we want to measure their probability. For example, if there are \(3\) identical balls in a bag with green, blue, and red colors, the probability of a green ball coming out is \(\frac{1}{3}\). In this example, three things can happen:

- The green ball comes out
- The blue ball comes out
- The red ball comes out

So, all possible states are equal \(3\).

- The sum of the probability of an event occurring and the probability of that event not occurring is one. For example, in rolling the dice, the sum of “probability of bringing six” (which is \(\frac{1}{6}\)) with “not the probability of bringing six” (which is \(\frac{5}{6}\)) becomes one.

### Finding Probability of an Event Example 1:

When a fair dice is thrown, what is the probability of getting

a)The number 2

b)A number that is a multiple of 2

**Solution:** a fair dice is an unbiased dice where each of the six numbers is equally likely to turn up. \(S\)={\(1, 2, 3, 4, 5, 6\)}

a)Let \(A=\)event of getting the number \(2=\){\(2\)}

Let \(nA=\)number of outcomes in event \(A=1\)

Let \(nS=\)number of outcomes in \(S=6→P(A)=\frac{n(A)}{n(S)}→P(A)=\frac{1}{6}\)

b)Let \(B=\)event of getting a multiple of \(2\)

multiple of \(2=\){\(2, 4, 6\)} \(→P(B)=\frac{3}{6}=\frac{1}{2}\)

### Finding Probability of an Event Example 2:

Each of the letters “SOLUTION” is written on a card. A card is chosen at random from the bag. What is the probability of getting the letter ‘O’?

**Solution:** Since the card is randomly selected, it means that each card has the same chance of being selected. \(S\)={\(S, O1, L, U, T, I, O2, N\)}

there are two cards with the letter ‘O’ Let \(A\) event of getting the letter ‘L’={\(O1, O2\)}

\(P(A)=\frac{2}{8}=\frac{1}{4}\)

## Exercises for Finding Probability of an Event

**Find the probability for the following events.**

- Six women and five men interviewed for a job. One of the candidates will be offered the job. Find the probability the job is offered to a woman.
- Jim is pulling marbles out of a box. There are 3 black marbles and 9 green marbles. Find the probability that Jim pulls out a green marble.

- Probability: \(\frac{6}{11}\)
- Probability: \(\frac{9}{12}=frac{3}{12}\)

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