Probability

Online MCQs Probability Quiz Answers. The Quiz covers topics of rules of counting, events, and types of events such as mutually exclusive and exhaustive events, sample space, Rules of Probability, etc. Let us start with the MCQs Probability Quiz Answers.

Online MCQs Probability Quiz Answers

• In how many ways can 6 persons be seated on a sofa set with three seats?
• The number of ways in which four books can be arranged on a shelf is
• Number of ways a committee of 3 members can be selected from 5 members
• $^nC_r=$
• $^5P_1=$
• Two events are called collectively exhaustive if $A\cup B=$
• If $A \cap B=\phi$, then the events $A$ and $B$ are called
• When a coin is tossed, the sample space is
• A coin is tossed three times in succession the number of sample points in the sample space is
• Three coins are tossed together, the sample will consist of ———- sample points.
• When a die and coin are rolled there are sample points.
• When a pair of dice is rolled, the sample space consists of
• Total number of ways when three fair dice are thrown
• If three cards are drawn from a pack of 52 cards, then sample space is
• The probability of an event always lies between
• The probability of an event cannot be
• The sum of probabilities of all mutually exclusive events of an experiment will be
• In tossing two perfect coins the probability that at least one head will occur is
• If a coin is tossed thrice then the probability of three heads is
• Three coins are tossed, ———- is the probability of getting at least one head.

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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

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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.

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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

Disadvantages of Subjective Probability

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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