Tags Class 12th

Class 12th

Get insights from 11.9k questions on Class 12th, answered by students, alumni, and experts. You may also ask and answer any question you like about Class 12th

Follow Ask Question

11.9k

Questions

Discussions

Active Users

Followers

New answer posted

a year ago

Class 12th Probability

Two events $E$ and $F$ are independent. If $P (E) = 0.3$ , $P (E \cup F) = 0.5$ , then $P (E ∣ F) - P (F ∣ E)$ equals:

0 Follower 5 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : E a n d F a r e t w o i n d e p e n d e n t e v e n t s s u c h t h a t \\ P (E) = 0.3, a n d P (E \cup F) = 0.5 \\ ∴ P (E \cup F) = P (E) + P (F) - P (E \cap F) \\ 0.5 = 0.3 + P (F) - P (E) . P (F) \\ \Rightarrow 0.5 - 0.3 = P (F) [1 - P (E)] \Rightarrow 0.2 = P (F) (1 - 0.3) \\ \Rightarrow 0.2 = P (F) . (0.7) \\ ∴ P (F) = \frac{0.2}{0.7} = \frac{2}{7} \\ N o w P (E / F) - P (F / E) = \frac{P (E \cap F)}{P (F)} . \frac{P (E \cap F)}{P (E)} \\ = \frac{P (E) . P (F)}{P (F)} . \frac{P (E) . P (F)}{P (E)} = P (E) - P (F) = \frac{3}{10} - \frac{2}{7} = \frac{1}{70} \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

0 0

New answer posted

a year ago

Class 12th Probability

If the events $A$ and $B$ are independent, then $P (A \cap B)$ is equal to:

$(a) P(A) +P (B)$

$(b) P(A) -P (B)$

$(c) P(A) \cdot P(B)$

$(d) P(A) ? P(B)$

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} A a n d B a r e t w o i n d e p e n d e n t e v e n t s \\ ∴ P (A \cap B) = P (A) . P (B) \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

0 0

New answer posted

a year ago

Class 12th Probability

Let $A$ and $B$ be two events such that $P (A) = \frac{3}{8}$ , $P (B) = \frac{5}{8}$ , and $P (A \cup B) = \frac{3}{4}$ . Then $P (A ∣ B) \cdot P (A^{'} ∣ B)$ is equal to:

0 Follower 4 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : P (A) = \frac{3}{8}, P (B) = \frac{5}{8} a n d P (A \cup B) = \frac{3}{4} \\ ∴ P (A \cup B) = P (A) + P (B) - P (A \cap B) \\ \frac{3}{4} = \frac{3}{8} + \frac{5}{8} - P (A \cap B) \\ \Rightarrow P (A \cap B) = \frac{3}{8} + \frac{5}{8} - \frac{3}{4} = \frac{1}{4} \\ N o w P (A / B) . P (A' / B) = \frac{P (A \cap B)}{P (B)} . \frac{P (A' \cap B)}{P (B)} \\ = \frac{P (A \cap B)}{P (B)} . \frac{P (B) - P (A \cap B)}{P (B)} \\ = \frac{\frac{1}{4}}{5} . \frac{(\frac{5}{8} - \frac{1}{4})}{5} = \frac{2}{5} . \frac{3}{5} = \frac{6}{25} \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

0 0

New answer posted

a year ago

Class 12th Probability

If two events are independent, then

(a) They must be mutually exclusive

(b) The sum of their probabilities must be equal to 1

(c) (a)and (b) both are correct

(d) None of the above is correct

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

0 0

New answer posted

a year ago

Class 12th Probability

If $A$ and $B$ are two independent events with $P (A) = \frac{3}{5}$ and $P (B) = \frac{4}{9}$ , then $P (A^{'} \cap B^{'})$ equals:

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : A a n d B a r e i n d e p e n d e n t e v e n t s \\ s u c h t h a t P (A) = \frac{3}{5} ∴ P (A') = 1 - \frac{3}{5} = \frac{2}{5} \\ P (B) = \frac{4}{9} ∴ P (B') = 1 - \frac{4}{9} = \frac{5}{9} \\ ∴ P (A' \cap B') = P (A') . P (B') = \frac{2}{5} . \frac{5}{9} = \frac{2}{9} \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

0 0

New answer posted

a year ago

Class 12th Probability

If $A$ and $B$ are such events that $P (A) > 0$ and $P (B) \neq 1$ , then $P (A^{'} ∣ B^{'})$ equals:

$(a) 1 - (∣)$

$(b) 1 - (' ∣)$

$(c) 1 - \frac{(\cap)}{(')}$

$P(A') ∣P (B')$

0 Follower 17 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : P (A) > 0 a n d P (B) \neq 1 \\ ∴ P (A' / B') = \frac{P (A' \cap B')}{P (B')} = \frac{1 - P (A \cup B)}{P (B')} \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

0 0

New answer posted

a year ago

Class 12th Probability

Let $P (A) = \frac{7}{13}$ , $P (B) = \frac{9}{13}$ , and $P (A \cap B) = \frac{4}{13}$ . Then $P (A^{'} ∣ B)$ is equal to:

0 Follower 4 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : \\ P (A) = \frac{7}{13}, P (B) = \frac{9}{13}, P (A \cap B) = \frac{4}{13} \\ P (A' / B) = \frac{P (A' \cap B)}{P (B)} = \frac{P (B) - P (A \cap B)}{P (B)} \\ = \frac{\frac{9}{13} - \frac{4}{13}}{\frac{9}{13}} = \frac{\frac{5}{13}}{\frac{9}{13}} = \frac{5}{9} \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

0 0

New answer posted

a year ago

Class 12th NEET

How does the Shiksha's NCERT Exemplar help in mastering Chapter 12 – Atoms?

0 Follower 2 Views

Pallavi Pathak

Contributor-Level 10

The NCERT Exemplar given on Shiksha's website provides a variety of numerical, conceptual and application-based questions around energy transitions, atomic models, and spectral series. It is a powerful study material for CBSE Board examination preparation and competitive exams like NEET and JEE.

0 0

New answer posted

a year ago

Class 12th Probability

If $P (B) = \frac{3}{5}$ , $P (A / B) = \frac{1}{2}$ , and $P (A \cup B) = \frac{4}{5}$ , then $P (A \cup B^{'}) + P (A^{'} \cup B)$ equals:

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t : \\ P (B) = \frac{3}{5}, P (A / B) = \frac{1}{2}, P (A \cup B) = \frac{4}{5} \\ P (A / B) = \frac{P (A \cap B)}{P (B)} \\ \Rightarrow \frac{1}{2} = \frac{P (A \cap B)}{\frac{3}{5}} \Rightarrow P (A \cap B) = \frac{3}{10} \\ P (A \cup B) = P (A) + P (B) - P (A \cap B) \\ \frac{4}{5} = P (A) + \frac{3}{5} - \frac{3}{10} \\ P (A) = \frac{4}{5} - \frac{3}{5} + \frac{3}{10} = \frac{1}{5} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2} \\ N o w P (A \cup B)' + P (A' \cup B) \\ = 1 - P (A \cup B) + 1 - P (A \cap B') \\ = 2 - \frac{4}{5} - P (A) . P (B') \\ = \frac{6}{5} - \frac{1}{2} . (1 - \frac{3}{5}) = \frac{6}{5} - \frac{1}{2} * \frac{2}{5} = \frac{6}{5} - \frac{1}{5} = \frac{5}{5} = 1 \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

0 0

New answer posted

a year ago

Class 12th NEET

According to Bohr's theory, why do electrons not fall into the nucleus?

0 Follower 1 View

Pallavi Pathak

Contributor-Level 10

According to Bohr's postulates, in specific stable orbits, electrons revolve without emitting energy. Energy is only absorbed or emitted when electrons jump between these orbits, preventing them from spiraling into the nucleus.

0 0

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

66k Colleges
1.2k Exams
703k Reviews
1850k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Need guidance on career and education? Ask our experts

Your Question

Class 12th

Questions

Discussions

Active Users

Followers

All

Discussions

Unanswered Questions

Share Your College Life Experience