Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If four persons independently solve a certain problem correctly with probabilities <img alt="\mathrm{\frac{1}{2}, \frac{3}{4}, \frac{1}{4} \: and \: \frac{1}{8},}" src="https://entrancecorner.oncod

If four persons independently solve a certain problem correctly with probabilities \mathrm{\frac{1}{2}, \frac{3}{4}, \frac{1}{4} \: and \: \frac{1}{8},}then the probability that the problem is solved correctly by atleast one of them, is
 

Option: 1

\frac{235}{256}

 


Option: 2

\frac{21}{256}
 


Option: 3

\frac{3}{256}
 


Option: 4

\frac{253}{256}


Answers (1)

best_answer

\mathrm{P} (problem solved correctly by atleast one)

\mathrm{=1-P} (problem is not solved by all)

\mathrm{=1-P(\bar{A} \cap \bar{B} \cap \bar{C} \cap \bar{D})}

\mathrm{=1-P(\bar{A}) P(\bar{B}) P(\bar{C}) P(\bar{D})}
[if \mathrm{A, B, C \: and \: D} are independent events, then \mathrm{\bar{A}, \bar{B}, \bar{C} \: and\: \bar{D}} are also independent events]

\mathrm{=1-\left(\frac{1}{2}\right)\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)\left(\frac{7}{8}\right)=1-\frac{21}{256}=\frac{256-21}{256}=\frac{235}{256}}

Hence option 1 is correct.

Posted by

Info Expert 30

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 session 2 application correction begins on jeemain.nta.nic.in; edit details by tomorrow
anam-khan

JEE Main 2026 Registration LIVE: Session 2 exam from April 2 to 9; shift timings, admit card, exam pattern
anam-khan

JEE Main 2026 session 2 registration ends today for BTech, BArch; apply at jeemain.nta.nic.in

Latest Question