Question

If odds against solving a question by three students are 2:1, 5:2 and 5:3 , respectively, then probability that the question is solved only by one student is

• A. 31/56
• B. 24/56
• C. 25/56
• D. none of these

Answer 1

The correct option is C 25/56

Given, $P\left(A\right)=\frac{1}{3},P\left(B\right)=\frac{2}{7},P\left(C\right)=\frac{3}{8}$

Probability that the question is solved only by one student is

$=P\left(A\right)\times P(B{)}^c\times P(C{)}^c+P(A{)}^c\times P(B)\times P(C{)}^c+P(A{)}^c\times P(B{)}^c\times P\left(C\right)$

$=(\frac{1}{3}\times \frac{5}{7}\times \frac{5}{8})+(\frac{2}{3}\times \frac{2}{7}\times \frac{5}{8})+(\frac{2}{3}\times \frac{5}{7}\times \frac{3}{8})=\frac{25}{56}$