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.
Online MCQs about Probability with Answers
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 $P(B|A)=$?
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.
Table of Contents
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
Define empirical probability.
How can one compute empirical probability? Write the formula of empirical probability.
Give real-life examples of empirical/ experimental probability.
What are the limitations of empirical/ experimental probability?
How does empirical/ experimental probability resemble frequency distribution? explain.
Different between classical probability and experimental probability.
Online MCQs Probability Questions and 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 Questions and Answers.
