Probability Examples and Solutions
We have provided you with some probability problems with their solutions.
Example 1: There are 8 balls in a container, 4 are red, 1 is yellow and 3 are blue. What is the probability of picking a yellow ball?
Probability of picking a ball
Solution:
Probability is equal to the number of yellow balls in the container divided by the total number of balls in the container, i.e. 1/8.
Example 2: A dice is rolled. What is the probability that an even number has been obtained?
Probability of Rolling a Dice
Solution:
When fair six-sided dice are rolled, there are six possible outcomes: 1, 2, 3, 4, 5, or 6.
Out of these, half are even (2, 4, 6) and half are odd (1, 3, 5). Therefore, the probability of getting an even number is:
P(even) = number of even outcomes / total number of outcomes
P(even) = 3 / 6
P(even) = 1/2
Example 3: A bag contains 4 white, 5 red, and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
Solution:
Let S be the sample space.
Then, n(S) = Number of ways of drawing 3 balls out of 15
n(S) = 15C3 = 455
Let E = event of getting all the 3 red balls.
n(E) = 5C3 = 10
P(E) = n(E)/n(S) = 10/455 = 2/91.
Example 4: In a class, there are 10 girls and 15 boys, what is the probability that 1 girl and 2 boys are selected?
Solution:
Let S be the sample space.
Then, n(S) = Number of ways of selecting 3 children out of 25
n(S) = 25C3
n(S) = 2300.
Let E= event of selecting 1 girl and 2 boys.
n(E) = 10C1*15C2 = 1050
P(E) = n(E)/n(S) = 1050/2300 = 21/46.
Probability in Maths
Probability is a field of mathematics that deals with events and quantifies their likelihood of occurring with numerical values ranging from 0 to 1. Higher probabilities indicate a greater chance of the event happening. It is expressed as a number between 0 and 1.
In this article, we will discuss what is probability in maths, its definition, formula, types, theorems, and solved examples on probability.
Table of Content
- What is Probability in Maths?
- Probability Definition
- Probability Theory
- Terms in Probability
- Probability of an Event
- Types of Events in Probability
- Probability Formula
- Probability Tree Diagram
- Types of Probability
- Theoretical Probability
- Experimental Probability
- Axiomatic Probability
- Probability Theorems
- Bayes’ Theorem on Conditional Probability
- Bayes Theorem Formula
- Probability Density Function
- Common Probability Problems
- Probability Examples and Solutions