Probability

The post is about the MCQs Probability Test. There are 20 multiple-choice questions covering topics related to the Basics of Probability, addition and multiplication rules of probability, events, and types of events. Let us start with MCQs Probability Quiz with Answers.

MCQs Probability Quiz with Answers

• If $A$ and $B$ are mutually exclusive events with $P(A) = 0.3$ and $P(B) = 0.5$, then $P(A \cup B) =?$
• In an experiment, $A$ and $B$ are mutually exclusive events, if $P(A)=0.6$, then the probability of $B$
• Which of the following statements is(are) always true?
• One of the basic requirements of probability is
• Events $A$ and $B$ are mutually exclusive with $P(A)=0.3$ and $P(B) = 0.2$. The probability of the complement of Event $B$ equals
• The multiplication law is potentially helpful when we are interested in computing the probability of
• If $P(A) =0.80$, $P(B)=0.65$, and $P(A\cup B) = 0.78$, then $P(B|A) =$?
• If two events are independent, then
• If $A$ and $B$ are independent events with $P(A)=0.38$ and $P(B)=0.55$, then $P(A|B)=$?
• If $X$ and $Y$ are mutually exclusive events with $P(X) = 0.295, P(Y) = 0.32$, then $P(X|Y)=$?
• What is the probability that a ball is drawn at random from a jar?
• In statistics, a number between ———- is used to express the probability that an event will occur.
• Two events are ———- if the occurrence of one event changes the probability of the other event.
• What does Bayes’s theorem enable data professionals to calculate?
• What is conditional probability?
• Suppose two events occur: The first event is drawing an ace from a standard deck of playing cards, and the second event is drawing another ace from the same deck. Note that the first ace is not reinserted into the deck after it is drawn. What term is used to describe these two events?
• ———— probability is the updated probability of an event based on new data.
• The probability of rain tomorrow is 40%. What is the probability of the complement of this event?
• Two events are ———– if the occurrence of one event does not change the probability of the other event.
• A jar contains four marbles: Two marbles are red, one is green, and one is blue. One marble is taken from the jar. What is the probability that the marble is blue?

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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.

Please go to Important MCQs Probability Quiz 2 to view the test

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: Let 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: Let 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.

FAQS about Empirical/ Experimental Probability

1. Define empirical probability.
2. How one can 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 with frequency distribution, explain.

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