>
Exams
>
Mathematics
>
Probability
>
the probability of impossible events is
Question:
The probability of impossible events is:
Show Hint
An impossible event corresponds to the empty set, which always has probability 0.
UP Board XII - 2026
UP Board XII
Updated On:
Sep 23, 2026
\(0\)
\(\dfrac12\)
\(\dfrac13\)
\(\dfrac14\)
Show Solution
Verified By Collegedunia
The Correct Option is
A
Solution and Explanation
Step 1: Understanding the Concept:
An impossible event is one that can never occur; it corresponds to the empty set \(\varnothing\) in the sample space.
Step 2: Applying the probability axiom:
By the axioms of probability, \(P(\varnothing)=0\).
Final Answer:
\[ \boxed{0} \]
Download Solution in PDF
Was this answer helpful?
0
0
Top UP Board XII Mathematics Questions
(c) Solve the differential equation \( (\tan^{-1} y - x) dy = (1 + y^2) dx \):
UP Board XII - 2024
Mathematics
Algebra
View Solution
(d) If \( (\cos x)^y = (\cos y)^x \), find \( \frac{dy}{dx} \):
UP Board XII - 2024
Mathematics
Algebra
View Solution
(e) If \( y = x \cos (a + y) \) and \( \cos a \neq \pm 1 \), prove that
\[ \frac{dy}{dx} = \frac{\cos^2 (a + y)}{\sin a}. \]
UP Board XII - 2024
Mathematics
Algebra
View Solution
(a) If a die is thrown three times, find the probability of getting one appearing number in them will be odd:
UP Board XII - 2024
Mathematics
Probability and Statistics
View Solution
(b) Minimize \( Z = x + 2y \) under the following constraints:
\[ 2x + y \geq 3, \quad x + 2y \geq 6, \quad x \geq 0, \quad y \geq 0. \]
UP Board XII - 2024
Mathematics
Optimization
View Solution
View More Questions
Top UP Board XII Probability Questions
There are 4 white and 2 black balls in a bag and in another bag 3 white and 5 black balls. Find the probability of getting both black balls if a ball is drawn from each bag.
UP Board XII - 2025
Mathematics
Probability
View Solution
The probability of solving a question by the three students A, B, C are respectively \( \frac{3}{10}, \frac{1}{5} \) and \( \frac{1}{10} \). Find the probability of solving the question.
UP Board XII - 2025
Mathematics
Probability
View Solution
If P(A) = 0.3, P(B) = 0.4, then find P(A/B) if A and B are independent events.
UP Board XII - 2025
Mathematics
Probability
View Solution
There are three groups of children having 3 girls and one boy, 2 girls and 2 boys, one girl and 3 boys respectively. One child is selected at random from each group. Find the probability that the three selected children have one girl and 2 boys.
UP Board XII - 2025
Mathematics
Probability
View Solution
Given any two events A and B are such that \( P(A) = \frac{1}{2}, P(B) = \frac{1}{4} \) and \( P(A \cap B) = \frac{1}{8} \), then find \( P(\text{not A and not B}) \).
UP Board XII - 2025
Mathematics
Probability
View Solution
View More Questions
Top UP Board XII Questions
In which one of the following States of India is the density of population the highest?
UP Board XII - 2024
Population
View Solution
Which one of the following States of India has the largest urban population?
UP Board XII - 2024
Population
View Solution
Which one of the following States is not related to the production of mineral oil?
UP Board XII - 2024
Resources and Industries
View Solution
Which one of the following sea ports is located on the eastern coast of India?
UP Board XII - 2024
Transportation
View Solution
What is meant by ‘Humanisation of Nature’?
UP Board XII - 2024
Human Geography
View Solution
View More Questions