In the field of Probability, an event is said to be a set of possible outcomes from random experiments. Whenever a random experiment is performed and the outcomes can not be predicted easily, in that case, we prefer to measure which of the events is more likely or less likely to happen. A single or simple event in probability is an event that comprises a single result. For example: when we toss a coin, the possibility of getting a tail is a single event. The events or probability of something happening are often described with words like impossible, unlikely, certain, likely, equally likely etc.

In this article, we are going to learn what a single event in probability is with solved examples and practice questions.

What is Event in Probability?

Events in Probability is the set of possible outcomes of any random experiments. For example: the possibility of getting even-numbered outcomes when we roll a dice is an event. Events are the subsets of sample space. The possibility of an event occurring is always between 0 and 1 and can include only 0 and 1.

• An event is impossible if it has a probability of 0. For example: having 13 months in a year has the probability of 0.
• An event is certain if it has a probability of 1. For example: the probability that the sun will rise tomorrow morning is 1.

For example: If we toss a coin, what are the possibilities of getting head as an outcome?

It only has two possibilities: heads or tails. So, the probability that heads will occur is one out of the two possibilities. In this case, both outcomes are equally likely or equally unlikely.

Single Event in Probability

A single event or a simple event is an event which comprises a single result from the sample space of an experiment. It is the opposite of a compound event which comprises more than a single event as an outcome.

For example: the sample space for rolling a dice, S = { 1, 2, 3, 4, 5, 6} in which the event of getting less than number 2 is one, that is A = {1}, where A is a single result taken from the sample space. Therefore this event is single or simple.

Formula for Event in Probability

To find the probability of a particular event, we use the following formula:

Event = \frac{number of favorable outcomes}{total number of outcomes}

Single Event Probability Worksheet

Question 1: What is the probability of getting 5 by rolling a six-sided dice?

Solution:

Sample space, S = {1, 2, 3, 4, 5, 6}

Total no. of favorable outcomes = 1

Total no. of possible outcome = 6

Probability P(5) = \frac{number of favorable outcomes}{total number of outcomes}

= \frac{1}{6}

Question 2: What is the probability of drawing an ace from a deck of 52 cards?

Solution:

Sample space, S = 52

Number of possible outcomes = 4

Probability, P = \frac{4}{52}

= \frac{1}{13}

Question 3: If we toss a fair coin, what are the probabilities of getting tails?

Solution:

Sample space, S = { head, tail}

Number of favorable outcomes = 1 ( since there is only one head in a coin)

Number of total outcomes = 2

Probability, P = \frac{1}{2}

Question 4: What is the probability of rolling a sum of 7 by rolling two dice?

Solution:

Sample space = 6× 6 = 36 outcomes are possible

Number of favorable outcomes = {(1,6), (3,4), (2,5), (5,2), (6,1), (4,3)}= 6 outcomes

Probability, P(sum of 7) = \frac{6}{36}

= \frac{1}{6}

Question 5: A bag contains 2 red marbles, 6 blue marbles, and 2 green marbles. What is the probability of drawing a green marble?

Solution:

Sample space = 2+6+2 = 10

Number of favorable outcomes = 2(since there are 2 green marbles)

Probability, P(red marble) = \frac{2}{10}

= \frac{1}{5}

Question 6: A whole number from 1 to 20 is picked randomly. What is the probability of getting prime numbers among them?

Solution:

Sample space = 20

Number of favorable outcomes = {2, 3, 5, 7, 11, 13, 17, 19} = 8 events

Probability, P = \frac{8}{20}

= \frac{2}{5}

Question 7: A set of numbers from 1 to 6 is picked. What is the probability of getting an even number?

Solution:

Sample space = 6

Number of favorable outcomes = {2,4,6} = 3 events

Probability, P = \frac{3}{6}

= \frac{1}{2}

Question 8: Two dice are thrown. Find the probability of getting the sum of numbers on the two dice is a perfect square.

Solution:

Sample space = 6× 6 = 36 total outcomes

Number of favorable outcomes = {(2, 2), (1, 3), (3, 1), (3, 6), (6, 3), (4, 5), (5, 4)} = 7 events

Probability, P = \frac{7}{36}

Question 9: The following cards are placed in a row: 1, 2, 3, 4, 5, 6. A card is selected at random. Find the probability that the number on the card is 3.

Solution:

Sample space = {1,2,3,4,5,6}= 6 events

Number of favorable outcomes = 1 event

Probability, P = \frac{1}{6}

Question 10: The following cards are placed in a row: 1, 2, 3, 4, 5, 6. A card is selected at random. Find the probability that the number on the card is an odd number.

Solution:

Sample space = {1,2,3,4,5,6} = 6 events

Number of favorable outcomes = 3 events

Probability, P = \frac{3}{6}

= \frac{1}{2}

A bag contains 10 discs. Each disc is labelled with a different number from 1 to 10. A disc is chosen from the bag at random.

Question 11: The probability that the chosen disc is the number 3

Solution:

Sample space = {1,2,3,4,5,6,7,8,9,10} = 10 events

Number of favorable outcomes = 1 event

Probability = \frac{1}{10}

Question 12: The probability that the chosen disc is a square number.

Solution:

Sample space = {1,2,3,4,5,6,7,8,9,10} = 10 events

Number of favorable outcomes = 2events

Probability = P = \frac{2}{10}

= \frac{1}{5}

Question 13: The probability that the chosen disc is a prime number.

Solution:

Sample space = {1,2,3,4,5,6,7,8,9,10} = 10 events

Number of favorable outcomes = {2,3,5,7} = 4events

Probability = P = \frac{4}{10}

= \frac{2}{5}

Question 14: The probability that the chosen disc is a number less than 5.

Solution:

Sample space = {1,2,3,4,5,6,7,8,9,10} = 10 events

Number of favorable outcomes = {1,2,3,4} = 4events

Probability = P = \frac{4}{10}

= \frac{2}{5}

Read More:

• Dependent and Independent Events
• Types of Events in Probability
• Chance and Probability

Practice Questions on Single Event Probability

Q1. What is the probability of a randomly chosen two-digit number being divisible by 6?

Q2. What is the probability that it is a red card ?

Q3. What is the probability of the seven of hearts ?

Q4. What is the probability that it is an even number ?

Q5. How many times would you expect to obtain an even score?

Q6. How many times would you expect to obtain a score less than 5?

Q7. How many times would you expect to obtain a 4?

Q8. What is the probability that the sweet is not red?

Q9. What is the probability that the sweet is green or yellow?

Q10. A spinner with five equally likely outcomes is spun. The outcomes are 1, 2, 3, 4 and 5. What is the probability of getting a two?

FAQs on Single Event Probability

How to calculate single event probability?

To find the probability of a singular event, we use the following formula:

Single Event = \frac{number of favorable outcomes}{total number of outcomes}

Single Event =\frac{a}{b}

What are the 4 types of probability?

The 4 types of probability are as follows:

• Classical Probability,
• Empirical Probability,
• Subjective Probability,
• Axiomatic Probability

Name different types of events.

We know that events are basically set, so they can be classified on the basis of the elements they have. The types of events are as follows:

• Impossible and Sure Events
• Simple Event and Compound Event
• Dependent and Independent Events
• Mutually Exclusive Events
• Exhaustive Events
• Equally Likely Events

Who is the father of probability?

Blaise Pascal is known as the father of probability. He received the problem of points from Gombaud. He sent a letter to Pierre de Fermat to ask for help in solving the Unfinished Game Problem. This led to the invention of probability.

What are the possible outcomes of a single event ?

The possibility of a single event occurring is always between 0 and 1 and can include only 0 and 1. An event is impossible if it has a probability of 0. For example: having 13 months in a year has the probability of 0. An event is certain if it has the probability of 1. For example: the probability that the sun will rise tomorrow morning is 1.