Probability

Online MCQs Probability Quiz with Answers. There are 20 multiple-choice questions covering topics related to the addition rule of probability, multiplication rule of probability, conditional probability, random experiment, and objective and subjective probability. Let us start with the MCQs Probability Quiz.

MCQs Probability Quiz with Answers

• Which of the following is not a correct statement about a probability
• The collection of one or more outcomes from an experiment is called
• If the occurrence of one event means that another cannot happen, then the events are
• In which approach to probability the outcomes are equally likely to occur?
• In the special rule of addition of probability, the events are always
• The joint probability is
• The special rule of multiplication of probability, the events must be
• A listing of the possible outcomes of an experiment and their corresponding probability is called
• Which of the following is not an example of a discrete probability distribution?
• Which of the following is not a condition of the binomial distribution?
• In a Poisson probability distribution
• If a card is chosen from a standard deck of cards, what is the probability of getting a five or a seven?
• If you roll a pair of dice, what is the probability that (at least) one of the dice is a 4 or the sum of the dice is 7?
• If a card is chosen from a standard deck of cards, what is the probability of getting a diamond (♦) or a club(♣)?
• The probability of occurrence of an event lies between
• The tail or head, one or zero, and girl and boy are examples of
• If $P(E)$ is the probability that an event will occur, which of the following must be false?
• The addition rule states that, if the events $A$ and $B$ are ———-, then the probability of $A$ or $B$ happening is the sum of the probabilities of $A$ and $B$.
• Objective probability is based on personal feeling, experience, or judgment.
• The probability of no snow equals 1 minus the probability of snow. This is an example of what rule of probability?

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The post contains MCQs Probability Questions with Answers. There are 20 multiple-choice questions covering topics related to the statistical experiment, basics of probability, sample space, addition rule of probability, multiplication rule of probability, and conditional probability. Let us start with MCQs Probability Questions.

Please go to Important MCQs Probability Questions 1 to view the test

MCQs Probability Questions with Answers

• The Complement of $P(A|B)$ is
• The probability of an intersection of two events is computed by using the
• If two events $A$ and $B$ are mutually exclusive events, then
• The range of probability is
• In a statistical experiment, each time the experiment is repeated
• The set of all possible outcomes (sample points) is called
• The sample space (experimental outcomes) refers to
• An experiment that consists of tossing 4 coins successively. The number of sample points in this experiment is
• On a December day, the probability of snow is 0.30. The probability of a “cold” day is 0.50. The probability of snow and a “cold” is 0.15. Do snow and “cold” weather are independent events?
• If $P(A)=0.5$ and $P(B)=0.5$, then $P(A \cap B)$ is
• If $A$ and $B$ are independent events with $P(A)=0.6$ and $P(B)=0.6$, then $P(A \cap B)=$?
• If events $A$ and $B$ are independent events with $P(A)=0.2$ and $P(B)=0.6$, then $P(A \cup B)=$?
• If $A$ and $B$ are independent events with $P(A)=0.4$ and $P(B)=0.25$, then $P(A \cup B)=$?
• Events $A$ and $B$ are mutually exclusive. Which of the following statements is true?
• If events $A$ and $B$ are independent events with $P(A)=0.05$ and $P(B)=0.65$, then $P(A|B)=$?
• A six-sided die is tossed three times. The probability of observing three ones in a row is
• If $P(A|B)=0.3$
• If events $A$ and $B$ are independent events with $P(A)=0.1$ and $P(B)=0.4$, then
• If $P(A|B)=0.3$ and $P(B)=0.8$, then
• If $P(A)=0.6$, $P(B)=0.3$, and $P(A \cap B)=0.2$, then $P(B|A)=$?

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Introduction to Empirical Probability

An empirical probability (also called experimental probability) is calculated by collecting data from past trials of the experiments. The experimental probability obtained is used to predict the future likelihood of the event occurring.

Formula and Examples Empirical/ Experimental Probability

To calculate an empirical/ experimental probability, one can use the formula

$$P(A)=\frac{\text{Number of trials in which $A$ occurs} }{$\text{Total number of trials}}$$

• Coin Flip: Let us flip a coin 200 times and get heads 105 times. The empirical probability of getting heads is $\frac{105}{200} =$ 0.525%, or 52.5%.
• Weather Prediction: Lets you track the weather for a month and see that it rained 12 out of 30 days. The empirical probability of rain on a given day that month is $\frac{12}{30} = 0.4$ or 40%.
• Plant Growth: Lets you plant 50 seeds and 35 sprout into seedlings. The experimental probability of a seed sprouting is $\frac{35}{50} = 0.70$ or 70%.
• Board Game: Suppose you play a new board game 10 times and win 6 times. The empirical probability of winning the game is $\frac{6}{10} = 0.6$ or 60%.
• Customer Preferences: In a survey of 100 customers, 80 prefer chocolate chip cookies over oatmeal raisins. The empirical probability of a customer preferring chocolate chip cookies is $\frac{80}{100} = 0.80$ or 80%.
• Basketball Game: A basketball player practices free throws and makes 18 out of 25 attempts. The experimental probability of the player making their next free throw is $\frac{18}{25} = 0.72$ or 72%.

Empirical Probability From Frequency Tables

A frequency table calculates the probability that a certain data value falls into any data group or class. Consider the frequency table of examination scores in a certain class.

Class	Frequency ($f$)	$frf$
40 – 49	1	$\frac{1}{20}=0.05$
50 – 59	2	$\frac{1}{20}=0.10$
60 – 69	3	$\frac{3}{20}=0.15$
70 – 79	4	$\frac{4}{20}=0.20$
80 – 89	6	$\frac{6}{20}=0.30$
90 – 99	4	$\frac{4}{20}=0.20$

Let event $A$ be the event that a student scores between 90 and 99 on the exam, then

$$P(A) = \frac{\text{Number of students scoring 90-99}}{\text{Total number of students}} = \frac{4}{20} = 0.20$$

Notice that $P(A)$ is the relative frequency of the class 90-99.

Key Points Empirical/ Experimental Probability

• It is based on actual data, not theoretical models.
• It is a good approach when the data is from similar events in the past.
• The more data you have, the more accurate the estimate will be.
• It is not always perfect, as past results do not guarantee future outcomes.

Limitations Empirical/ Experimental Probability

• It can be time-consuming and expensive to collect enough data.
• It may not be representative of the future, especially if the underlying conditions change.

Empirical Probability vs Classical Probability

Feature	Classical Probability	Empirical Probability
Definition	Based on logical reasoning and known outcomes	Based on actual data or experiments
Formula	$P(A)=\frac{\text{Favorable outcomes}}{\text{Total possible outcomes}}$​	$P(E)=\frac{\text{Observed frequency}}{\text{Total number of trials}}$
Based on	Theory / Assumptions	Observations / Real-world data
Requires Equal Likelihood?	Yes	No
When is it used?	Before an experiment is conducted	After performing experiments or collecting data
Example	Rolling a 6 on a fair die: $\frac{1}{6}$	Getting heads 45 times in 100 coin tosses: $\frac{45}{100}$​
Use Case	Games of chance, ideal conditions	Real-world scenarios, historical data analysis

FAQS about Empirical/ Experimental Probability

1. Define empirical probability.
2. How can one compute empirical probability? Write the formula of empirical probability.
3. Give real-life examples of empirical/ experimental probability.
4. What are the limitations of empirical/ experimental probability?
5. How does empirical/ experimental probability resemble frequency distribution? explain.
6. Different between classical probability and experimental probability.

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