Question

Wds against an event of solving a question by A is $4:3\&$ odds in favour of solving the same question by 'B' is $7:5$. If both A and $B$ solve the question. Then the probability that both solve the question.

• A. $1/4$
• B. $5/2$
• C. $16/2$
• D. none of these

Answer 1

The correct option is A $1/4$

$oddsagainstAofsolvingquestion=\left(\frac{4}{3}\right)\therefore P\left(Asolved\right)=\left(\frac{3}{3+4}\right)=\left(\frac{3}{7}\right)oddsinfavourofsolvingquestionbyB=\left(\frac{7}{5}\right)\therefore P\left(Bsolved\right)=\left(\frac{7}{7+5}\right)=\left(\frac{7}{12}\right)P\left(bothsolved\right)=P\left(Asolved\right)\times P\left(Bsolved\right)=\left(\frac{3}{7}\right)\times \left(\frac{7}{12}\right)=\left(\frac{1}{4}\right)$