Another word for probability is possibility. It is a math of chance, that deals with the happening of a random event. The value is indicated from zero to one. In math, Probability has been introduced to predict how likely events are to occur. The meaning of probability is basically the scope to which something is to be expected to happen.
Probability
To understand probability more accurately, take an example as rolling a dice, the possible outcomes are – 1, 2, 3, 4, 5, and 6. The probability of getting any of the possible outcomes is 1/6. As the probability of happening any of a possible event is the same so there are equal chances of getting any likely number in this case it is either 1/6 or 50/3.
Formula of Probability
Probability of an event = {Number of ways it can occur} ⁄ {Total number of outcomes}
P(A) = {Number of ways A occurs} ⁄ {Total number of outcomes}
Types of Events
There are different types of events based on different criteria. One of the types is an equally likely event and a complimentary event. Then there are impossible and sure events. One type is a simple and compound event. There are independent and dependent events, mutually exclusive, exhaustive events, etc. Let’s take a look at these events in detail.
- Equally Likely Events: After rolling a dice, the possibility of getting any of the equally likely events is 1/6. As the happening of an event is an equally likely event so there is equal or the same possibility of obtaining any number, in this case, it is either 1/6 in fair dice rolling.
- Complementary Events: There is a chance or possibility of only two results which is an event will occur or not. Like a person will study or not study, cleaning a car or not cleaning a car, etc. are examples of complementary events.
- Impossible and Sure Events: If the probability of happening of a likely event is 0, such an event is called an impossible event and if the probability of happening of a likely event is 1, it is called a sure event. In other words, the empty set ϕ is an impossible event and the sample space S is a sure event.
- Simple Events: Any event containing a single point of the sample space is known as a simple event in probability. For example, if S = {46 , 75 , 86 , 64 , 99} and E = {75} then E is a simple event.
- Compound Events: Opposite to the simple event, if any event contains more than one single point of the sample space then such an event is called a compound event. Considering the same example again, if S = {56, 78, 96, 54, 89}, E1 = {56, 54 }, E2 = {78, 56, 89} then, E1 and E2 represent two compound events.
- Independent Events and Dependent Events: If the occurrence of any event is completely unaffected by the occurrence of any other event, such events are known as independent events in probability and the events which are affected by other events are known as dependent events.
- Mutually Exclusive Events: If the occurrence of one event keeps out the occurrence of another event, such events are mutually exclusive events i.e. two events don’t have any common number. For example, if S = {5,6,7,8,9,10} and E1, E2 are two events such that E1 consists of numbers less than 7 and E2 consists of numbers greater than 8. So, E1 = {5,6,7} and E2 = {8,9,10} . Then, E1 and E2 are mutually exclusive.
- Exhaustive Events: A set of events is called exhaustive, which means that one of them must occur.
- Events Associated with “OR”: If two events E1 and E2 are associated with OR then it means that either E1 or E2 or both. The merging symbol (∪) is used to represent OR in probability. Thus, the event E1 U E2 indicates E1 OR E2. If we have mutually exhaustive events E1, E2, E3 …En associated with sample space S then, E1 U E2 U E3 U … En = S
- Events Associated with “AND”: If two events E1 and E2 are associated with AND then it means the joining of elements that is common to both the events. The intersection symbol (∩) is used to represent AND in probability. Thus, the event E1 ∩ E2 indicates E1 and E2.
- Event E1 but not E2: It represents the difference between two of the events. Event E1 but not E2 show all the end results which are present in E1 but not in E2. Thus, the event E1 but not E2 is represented as E1, E2 = E1 – E2
What is the mean outcome if a fair six-sided die is rolled once?
Solution:
After rolling the dice the possible outcomes are 1,2,3,4,5,6
So, formula of mean = Sum of the terms ⁄ No. of terms
Mean outcome = 1 + 2 + 3 + 4 + 5 + 6 ⁄ 6
Mean outcome = 21 ⁄ 6
Mean outcome = 3.5
Similar Questions
Question 1: What is the even outcome if a fair six-sided die is rolled once?
Solution:
When rolling a fair six-sided die the total possible outcome are 1,2,3,4,5,6
And the even possible outcome are (2,4,6) in rolling one six-sided die, rolling an even number could occur with one of three outcomes: 2, 4, and 6.
P(E) = {Number of ways it can occur} ⁄ {Total number of outcomes}
Number of ways it can occur = 3 (2,4,6)
total number of outcome = 6 (1,2,3,4,5,6)
P(E) = 3⁄6 = 1⁄2
Question 2: What is the odd outcome if a fair six-sided die is rolled once?
Solution:
When rolling a fair six sided die the total possible outcome are 1,2,3,4,5,6
And the odd possible outcome are (1,3,5) in rolling one six-sided die, rolling an odd number could occur with one of three outcomes: 1, 3, and 5.
P(E) = {Number of ways it can occur} ⁄ {Total number of outcomes}
Number of ways it can occur = 3 (1,3,5)
total number of outcome = 6 (1,2,3,4,5,6)
P(E) = 3⁄6 = 1⁄2