Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain Solution R.D.Sharma Class 12 Chapter 30 Probability Exercise Multiple Choice Questions Question 60 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 30 Probability  Exercise Multiple Choice Questions  Question 60 Maths Textbook Solution.

Answers (1)

Answer:(a)

Hint: You must know the rules of finding probability.

Given: A and B are independent such that

\begin{aligned} &0<P(A)<1 \\ &0<P(B)<1 \end{aligned}

Solution: If A and B are independent

P(A \cap B)=P(A) \times P(B)

Now,

\begin{aligned} &P(A \cap \bar{B})=P(A)-P(A \cap B) \\ &=P(A)-P(A) P(B) \\ &=P(A)\{1-P(B)\} \\ &=P(A) P(\bar{B}) \end{aligned}

Hence \mathrm{A} and \overline{\mathrm{B}} are indepemdent

Similarly,

\begin{aligned} &P(\bar{A} \cap \bar{B})=1-P(A \cup B) \\ &=1-P(A) \times P(B)-P(A \cap B) \\ &=1-P(A) \times P(B)-P(A) P(B) \\ &=1(1-P(A))-P(B)\{1-P(A)\} \\ &=\{1-P(A)\}-\{1-P(B)\} \\ &=P(\bar{A})-P(\bar{B}) \end{aligned}

\text { Hence } \overline{\mathrm{A}} \text { and } \overline{\mathrm{B}} \text { are independent }

\begin{aligned} &P\left(\frac{A}{B}\right)+P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}+\frac{P(\bar{A} \cap B)}{P(B)} \\ &=\frac{P(A) P(B)+P(\bar{A}) P(B)}{P(B)} \\ &\text { and } 1-P(A)=P(\bar{A}) \\ &\therefore 1=P(A)+P(\bar{A}) \\ &\therefore \frac{P(A \cap B)}{P(B)}+\frac{P(\bar{A} \cap B)}{P(B)} \\ &=\frac{P(A) P(B)+P(\bar{A}) P(B)}{P(B)} \\ &=\frac{P(B)(P(A)+P(\bar{A}))}{P(B)} \\ &=1 \end{aligned}

\therefore Option \mathrm{A} is incorrect because \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(A) P(B) \neq 0

Since \mathrm{P}(A)>0 and P(B)>0

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO
anam-khan

Board Exam Date 2025 Live: CBSE, ICSE, BSEB, MPBSE Class 10, 12 timetable out; Punjab, Rajasthan schedule soon
anam-khan

CBSE Board Exams 2025: Guidelines issued for Class 10, 12 practicals

Latest Question