## Important Probability Online MCQs Test 6

This Quiz contains Probability Online MCQs Test, events, experiments, mutually exclusive events, collectively exhaustive events, sure events, impossible events, addition and multiplication laws of probability, etc. Let us start the Probability Online MCQs Test with the Answers:

Online MCQs Exam for the Post of PPSC Statistics Lecturer and Statistical Officer

1. A fair coin is tossed 50 times, and the expected number of heads is:

2. How would you calculate the probability that a random variable is less than 5?

3. What word describes two events that cannot occur at the same time?

4. The subset of a sample space is called

5. Events having an equal chance of occurrence are called

6. What is the expected value?

7. $P(A\cap B() = P(A) P(B|A)$, then $A$ and $B$ are

8. How would you describe $P(A|B)$ in words for two sets $A$ and $B$?

9. How would you describe $P(A \cap B)$ in words for two sets $A$ and $B$?

10. If $A$ and $B$ are dependent events, $P(A)=0.40$ and $P(B|A)=0.35$ then $P(A \cap B)$ is

11. In the context of probability, what is an outcome?

12. What is a random variable?

13. In the context of probability, what is a sample space?

14. What is conditional probability?

15. What is a probability?

16. A conditional probability might be found in which of the following ways?

17. The probability of an event happening is $\frac{1}{3}$. The probability of it not happening is?

18. What is a continuous random variable?

19. $A$ and $B$ are two mutually exclusive events. The probability of $A$ happening is $\frac{1}{4}$. The probability of $BB$ happening is $\frac{1}{3}$. The probability of neither $A$ nor $B$ happening is?

20. What shows the exact probabilities for a particular value of a random variable?

### Probability Online MCQs Test

• In the context of probability, what is an outcome?
• What is a probability?
• How would you calculate the probability that a random variable is less than 5?
• In the context of probability, what is a sample space?
• What word describes two events that cannot occur at the same time?
• What is the expected value?
• What is conditional probability?
• What is a continuous random variable?
• What shows the exact probabilities for a particular value of a random variable?
• How would you describe $P(A \cap B)$ in words for two sets $A$ and $B$?
• How would you describe $P(A|B)$ in words for two sets $A$ and $B$?
• What is a random variable?
• $A$ and $B$ are two mutually exclusive events. The probability of $A$ happening is $\frac{1}{4}$. The probability of $BB$ happening is $\frac{1}{3}$. The probability of neither $A$ nor $B$ happening is?
• The probability of an event happening is $\frac{1}{3}$. The probability of it not happening is?
• A conditional probability might be found in which of the following ways?
• A fair coin is tossed 50 times, and the expected number of heads is:
• If $A$ and $B$ are dependent events, $P(A)=0.40$ and $P(B|A)=0.35$ then $P(A \cap B)$ is
• $P(A\cap B() = P(A) P(B|A)$, then $A$ and $B$ are
• The subset of a sample space is called
• Events having an equal chance of occurrence are called

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## Best Online Probability Quizzes

This post contains MCQs about Online Probability Quiz, events, experiments, mutually exclusive events, collectively exhaustive events, sure events, impossible events, addition and multiplication laws of probability, etc. Let us start the MCQs Online Probability Quiz:

### Online Probability Quiz

Probability is concerned with how events are likely to occur. It is a way of assigning a numerical value between 0 (impossible event) and 1 (sure event) to represent the chance of something happening. The higher the probability, the more likely the event.

Some of the important probability terms:

• Event: An event is any outcome or set of outcomes from a random experiment.
• Favorable Outcome: An outcome that satisfies the event one is interested in.
• Independent Events: Events are considered independent if the outcome of one event does not affect the probability of the other event. For example, outcomes from Rolling a die and flipping a coin are independent events.
• Dependent Events: Events are said to be dependent if the outcome of one affects the probability of the other. For example, drawing a card from a standard deck of cars and then drawing another card without replacing the first one is an example of dependent events.

Probability and its computations are performed in many fields, including statistics, finance, gambling, and even artificial intelligence. Probability is a fundamental tool for making predictions and analyzing data under uncertainty.

## Subjective Probability (2019)

A type of probability based on personal beliefs, judgment, or experience about the occurrence of a specific outcome in the future. The calculation of subjective probability contains no formal computations (of any formula) and reflects the opinion of a person based on his/her experience. The subjective probability differs from subject to subject and it may contain a high degree of personal biases.

This kind of probability is usually based on a person’s experience, understanding, knowledge, and intelligence and determines the probability of some specific event (situation). It is usually applied in real-life situations, especially, related to the decision in business, job interviews, promotions of the employee, awarding incentives, and daily life situations such as buying and/or selling of a product. An individual may use their expertise, opinion, past experiences, or intuition to assign the degrees of probability to a specific situation.

It is worth noting that the subjective probability is highly flexible in terms of an individual’s belief, for example, one individual may believe that the chance of occurrence of a certain event is 25%. The same person or others may have a different belief especially when they are given a specific range from which to choose, (such as 25% to 30%). This can occur even if no additional hard data is behind the change.

### Events that may Alter Subjective Probability

Subjective probability is usually affected by a variety of personal beliefs and opinions (related to his caste, family, region, religion, and even relationship with people, etc.), held by an individual. It is because the subjective probability is often based on how each individual interprets the information presented to him

As only personal opinions (beliefs, experiences) are involved, there may be a high degree of bias. On the other hand, one person’s opinion may differ greatly from the opinion of another person. Similarly, in subjective probability, one may fall into the trap of failing to meet complex calculations.

### Examples Related to Subjective Probability

• One may think that there is an 80% chance that your best friend will call you today because his/her car broke down yesterday and he/she will probably need a ride.
• You think you have a 50% chance of getting a certain job you applied for as the other applicant is also qualified.
• The probability that in the next (say) 5 hours, there will be rain is based on current weather situations, wind patterns, nearby weather, barometric pressure, etc. One can predict this based on his experience with weather and rain, and believes, in predicting the rain in the next 5 hours.
• Suppose, a cricket tournament is going to be held between Pakistan and India. The theoretical probability of winning either the cricket team is 50%. But, in reality, it is not 50%. On the other hand (like empirical probability), the number of trial tournaments cannot be arranged to determine an experimental probability. Thus, the subjective probability will be used to find the winning team which will be based on the beliefs and experience of the investigator who is interested in finding the probability of the Pakistan cricket team as the winner. Note there will be a bias if any of the fans of a team investigates the probability of winning a team.
• To locate petroleum, minerals, and/ or water lying under the earth, dowsers are employed to predict the likelihood of the existence of the required material. They usually adopt some non-scientific methods. In such a situation, the subject probability is used.
• Note the decisions through subjective probability may be valid if the degree of belief of a person is unbiased about the situation and he/she arrives by some logical reasoning.

For further reading See Introduction to Probability Theory

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## Classical Probability: Example, Definition, and Uses (2017)

Classical probability is the statistical concept that measures the likelihood (probability) of something happening. In a classic sense, it means that every statistical experiment will contain elements that are equally likely to happen (equal chances of occurrence of something). Therefore, the concept of classical probability is the simplest form of probability that has equal odds of something happening.

### Classical Probability Examples

Example 1: The typical example of classical probability would be rolling a fair die because it is equally probable that the top face of the die will be any of the 6 numbers on the die: 1, 2, 3, 4, 5, or 6.

Example 2: Another example of classical probability would be tossing an unbiased coin. There is an equal probability that your toss will yield either head or tail.

Example 3: In selecting bingo balls, each numbered ball has an equal chance of being chosen.

Example 4: Guessing a multiple choice quiz (MCQs) test with (say) four possible answers A, B, C, or D. Each option (choice) has the same odds (equal chances) of being picked (assuming you pick randomly and do not follow any pattern).

### Classical Probability Formula

The probability of a simple event happening is the number of times the event can happen, divided by the number of possible events (outcomes).

Mathematically $P(A) = \frac{f}{N}$,

where, $P(A)$ means “probability of event A” (event $A$ is whatever event you are looking for, like winning the lottery, that is event of interest), $f$ is the frequency, or number of possible times the event could happen and $N$ is the number of times the event could happen.

For example,  the odds of rolling a 2 on a fair die are one out of 6, (1/6). In other words, one possible outcome (there is only one way to roll a 1 on a fair die) is divided by the number of possible outcomes.

Classical probability can be used for very basic events, like rolling a dice and tossing a coin, it can also be used when the occurrence of all events is equally likely. Choosing a card from a standard deck of cards gives you a 1/52 chance of getting a particular card, no matter what card you choose. On the other hand, figuring out whether will it rain tomorrow or not isn’t something you can figure out with this basic type of probability. There might be a 15% chance of rain (and therefore, an 85% chance of it not raining).

### Other Examples of classical Probability

There are many other examples of classical probability problems besides rolling dice. These examples include flipping coins, drawing cards from a deck, guessing on a multiple-choice test, selecting jellybeans from a bag, choosing people for a committee, etc.

### Classical Probability cannot be used:

Dividing the number of events by the number of possible events is very simplistic, and it isn’t suited to finding probabilities for a lot of situations. For example, natural events like weights, heights, and test scores need normal distribution probability charts to calculate probabilities. Most “real life” things aren’t simple events like coins, cards, or dice. You’ll need something more complicated than classical probability theory to solve them.

It is important to note that the classical probability is most applicable in situations where:

• All possible outcomes can be clearly defined and listed.
• Each outcome has an equal chance of happening.

In conclusion, classical probability provides a foundational understanding of probability concepts, and it has various applications in games of chance, simple random sampling, and other situations where clear, equally likely outcomes can be defined.