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

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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 probability of an event?

Probability measures how likely something is to happen, on a scale from 0 (impossible) to 1 (certain). For events with equally likely outcomes, \[P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}.\] Rolling a 4 on a fair six-sided die has probability \(1/6\), because there’s one favorable outcome (a 4) and six equally likely outcomes total.

How do you compute a basic probability?

Count the favorable outcomes, count the total outcomes, then divide. Example: drawing a red card from a standard 52-card deck. There are 26 red cards (favorable) out of 52 cards (total), so \(P(\text{red}) = 26/52 = 1/2\). Always reduce the fraction if you can – it makes the result easier to interpret.

What’s the difference between an event and an outcome?

An outcome is a single result of an experiment – say, rolling a 3. An event is a set of outcomes you care about – say, “rolling an even number.” The event “even” on a six-sided die contains the outcomes \(\{2, 4, 6\}\). Probability is computed for events, not just single outcomes.

What does probability 0 or 1 mean?

A probability of 0 means the event can’t happen – like rolling a 7 on a standard six-sided die. A probability of 1 means the event is certain – like rolling a number from 1 to 6 on that die. Anything in between is a real chance with some likelihood of happening.

What’s the complement rule?

The complement of an event \(A\) is everything in the sample space that isn’t \(A\). Their probabilities add to 1: \[P(\text{not } A) = 1 – P(A).\] If \(P(\text{rain tomorrow}) = 0.3\), then \(P(\text{no rain}) = 1 – 0.3 = 0.7\). The complement rule is often the fastest way to compute a probability when the “not” event is easier to count.

What’s a sample space?

The sample space is the set of all possible outcomes of an experiment. For flipping a coin, the sample space is \(\{\text{H}, \text{T}\}\). For rolling a standard die, it’s \(\{1, 2, 3, 4, 5, 6\}\). For rolling two dice, it’s the 36 ordered pairs \((1,1), (1,2), \ldots, (6,6)\). Listing the sample space is often the first step in tougher probability problems.

Can probabilities be written as percentages?

Yes – probabilities work as fractions, decimals, or percents. \(P = 1/4\), \(P = 0.25\), and \(P = 25\%\) all mean the same thing. Use whichever form fits the problem. Tests often ask for the form they want; pay attention so you don’t lose a point for a correct number in the wrong format.

What’s the difference between theoretical and experimental probability?

Theoretical probability comes from counting outcomes that are equally likely (a fair die has \(P(4) = 1/6\)). Experimental probability comes from actually running the experiment and counting what happens. If you roll a die 60 times and get a 4 twelve times, the experimental probability is \(12/60 = 0.2\). Over many trials, experimental probability approaches theoretical probability.

How do I find the probability of drawing a specific card?

Count favorable outcomes over total outcomes. A standard deck has 52 cards. \(P(\text{ace}) = 4/52 = 1/13\). \(P(\text{heart}) = 13/52 = 1/4\). \(P(\text{queen of hearts}) = 1/52\). For “ace OR heart,” use inclusion-exclusion: \(4/52 + 13/52 – 1/52 = 16/52 = 4/13\) (subtracting the ace of hearts that was double-counted).

Where does basic probability show up on tests?

Grade 6-8 state tests, the SAT, ACT, GED, HiSET, GRE, ASVAB, and most college placement and teacher-licensure tests. Common scenarios: dice, coins, cards, spinners, marbles in a bag, and word problems about populations. The math is light; the challenge is counting favorable and total outcomes accurately.

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