Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

\mathrm{P} and \mathrm{Q} are considering to apply for a job.The probability that \mathrm{P} applies for the job is \frac{1}{4}. The probability that \mathrm{P} applies for the job given that \mathrm{Q} applies for the job is \mathrm{\frac{1}{2}} , and the probability that \mathrm{Q} applies for the job given that \mathrm{P} applies for the job is \mathrm{\frac{1}{3}}. Then the probability that \mathrm{P} does not apply for the job given that \mathrm{Q} does not apply for the job is

 

Option: 1

\frac{4}{5}


Option: 2

\frac{5}{6}


Option: 3

\frac{7}{8}


Option: 4

\frac{11}{12}


Answers (1)

best_answer

\mathrm{A=\{P \text { applies for job }\},}
\mathrm{B=\{Q \text { applies for job }\}}

Then
\mathrm{P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}}\quad \cdots(1)
\mathrm{\text { \& } \quad P(B / A)=\frac{1}{3}}\quad \cdots (2)

Using (2)

\mathrm{\frac{P(B \cap A)}{P(A)} =\frac{1}{3} }
\mathrm{\Rightarrow \quad P(B \cap A) =\frac{1}{12} }

Using (1)

\mathrm{\quad \frac{P(B \cap A)}{P(B)} =\frac{1}{2}}
\mathrm{\Rightarrow \quad P(B) =\frac{1}{6}}

\mathrm{\text { So } \quad P\left(\frac{\bar{A}}{\bar{B}}\right) =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{B})}=\frac{1-P(A \cup B)}{1-P(B)} }
                               \mathrm{=\frac{1-\left(\frac{1}{4}+\frac{1}{6}-\frac{1}{12}\right)}{1-\frac{1}{6}}=\frac{2}{3} \times \frac{6}{5}=\frac{4}{5}}


 

Posted by

Gaurav

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: JCECEB invites fresh applications for Jharkhand state merit list correction

Latest Question