How to Find Probability of an Event? (+FREE Worksheet!)

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

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Step by step guide to Finding the 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 die 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})

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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.

1. Six women and five men were interviewed for a job. One of the candidates will be offered the job. Find the probability that the job is offered to a woman.
2. 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.

1. Probability: (frac{6}{11})
2. Probability: (frac{9}{12}=frac{3}{12})

Recommended EffortlessMath Books

For a complete grade-level workbook that covers data and statistics alongside the rest of pre-algebra, Pre-Algebra for Beginners walks you through statistics topics with clear examples and try-it-yourself problems. For more practice with data and probability at middle-school level, Mastering Grade 6 Math includes plenty of worked exercises.

Frequently Asked Questions

What is the formula to find the probability of an event?

The basic formula is P(event) = number of favorable outcomes ÷ total number of equally likely outcomes. For example, the probability of drawing a red marble from a bag with 3 red and 7 blue marbles is 3/10 = 0.3, or 30%. Every probability falls between 0, meaning impossible, and 1, meaning certain.

What is an event in probability?

An event is any outcome or group of outcomes you are interested in. When rolling a six-sided die, rolling a 4 is an event, and rolling an even number is also an event made of the outcomes 2, 4 and 6. The probability of rolling an even number is 3/6 = 1/2.

How do you find the probability of an event not occurring?

Subtract the probability of the event from 1: P(not A) = 1 − P(A). This is called the complement rule. If the chance of rain tomorrow is 0.35, the chance of no rain is 1 − 0.35 = 0.65. It works because an event and its complement together cover all possible outcomes.

How do you find the probability of event A and B?

If A and B are independent, multiply their probabilities: P(A and B) = P(A) × P(B). For example, the chance of flipping heads and rolling a 6 is 1/2 × 1/6 = 1/12. If the events are dependent, multiply P(A) by the probability of B after A has happened, as when drawing cards without replacement.

How do you find the probability of an event happening at least once?

Find the probability that it never happens, then subtract from 1. For example, the chance of rolling at least one 6 in two rolls of a die is 1 − (5/6 × 5/6) = 1 − 25/36 = 11/36, or about 0.31. This shortcut is much easier than listing every way the event could happen.

What is the probability of an event given another event?

This is conditional probability, written P(B | A), the chance of B given that A has already happened. The formula is P(B | A) = P(A and B) ÷ P(A). For example, if you draw a heart from a deck and keep it, the probability the next card is also a heart is 12/51 = 4/17.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to find the probability of an event
• How to solve probability problems
• How to find experimental probability
• Probability of simple and opposite events
• Conditional and binomial probabilities