Another word for probability is a 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 possibility of happening any of an 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%.
- Frequency interpretation: Probabilities are recognized as mathematically suitable estimations to long-run respective frequencies.
- Subjective interpretation: A probability statement indicates the belief of some person regarding how certain an event is likely to occur.
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 dice, the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is some possibility of obtaining any number in this case it is either 1/6 in fair dice rolling.
Complementary Events: There is a probability or possibility of only two outcomes which is an event will occur or not. Like a person will eat or not eat, buying a car or not buying 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 consisting of a single point of the sample space is known as a simple event in probability. For example, if S = {56, 78, 96, 54, 89} and E = {78} 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 excludes the occurrence of another event, such events are mutually exclusive events i.e. two events don’t have any common point. For example, if S = {1, 2, 3, 4, 5, 6} and E1, E2 are two events such that E1 consists of numbers less than 3 and E2 consists of numbers greater than 4.
So, E1 = {1, 2} and E2 = {5, 6}.
Then, E1 and E2 are mutually exclusive.
Exhaustive Events
A set of events is called exhaustive, it 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 union symbol (∪) is used to represent OR in probability. Thus, the event E1 U E2 indicates E1 OR E2. If mutually exhaustive events E1, E2, E3…En have 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 intersection of elements that is common to both the events. The joining 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 both 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 probability of rolling a zero on a fair dice?
Solution:
Pick up a regular dice. How many faces does it have: The answer should be 6. List the numbers available on the die: They should be 1, 2, 3, 4, 5, 6. Identify how many of those numbers are zero: I don’t see – so I make the count to be zero. When one has a set of discrete choices (one can only roll one number at a time on a dice) the probability is always going to be
Occurrences/total
Where occurrences are the number of different ways of achieving the outcome wanted. In this case, zero and total are the total number of discrete outcomes in this case 6. So the probability is 0⁄6 = 0. There are no numbers which are zero so achieving such an outcome is impossible
= Probability is zero.
Similar Problems
Question 1: What is the probability of rolling on a fair dice two?
Solution:
Pick up a regular dice. How many faces does it have: The answer should be 6. List the numbers available on the die: They should be 1, 2, 3, 4, 5, 6. Identify how many of those numbers are two: make the count be two.
When one has a set of discrete choices (one can only roll one number at a time on a dice) the probability is always going to be occurrences/total where occurrences are the number of different ways of achieving the outcome one wants. In this case, one and total is the total number of discrete outcomes in this case 6. So the probability is 1⁄6 = 0.16… There is only one number which is two,
= Probability is 1⁄6.
Question 2: What is the probability of rolling on a fair dice five?
Solution:
Pick up a regular dice. How many faces does it have: The answer should be 6. List the numbers available on the die: They should be 1, 2, 3, 4, 5, 6. Identify how many of those numbers are five: make the count be five.
When one has a set of discrete choices (one can only roll one number at a time on a dice) the probability is always going to be Occurrences/total where occurrences are the number of different ways of achieving the outcome one wants.
In this case, one and total is the total number of discrete outcomes in this case 6. So the probability is 1⁄6= 0.16…
There is only one number which is five,
= Probability is 1⁄6.
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