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 students is

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

Answer 1

The correct option is C $25/56$

The probability of solving the question by these three students are

$P\left(A\right)=\frac{1}{3},P\left(B\right)=\frac{2}{7},P\left(C\right)=\frac{3}{8}$ Then probability of question solved by only one student

$=P\left(A\overline{B}\overline{C}\text{or}\overline{A}B\overline{C}\text{or}\overline{A}\overline{B}C\right)$

$=P\left(A\right)P\left(\overline{B}\right)P\left(\overline{C}\right)+P\left(\overline{A}\right)P\left(B\right)P\left(\overline{C}\right)+P\left(\overline{A}\right)P\left(\overline{B}\right)P\left(C\right)$

$=\frac{1}{3}\times \frac{5}{7}\times \frac{5}{8}+\frac{2}{3}\times \frac{2}{7}\times \frac{5}{8}+\frac{2}{3}\times \frac{5}{7}\times \frac{3}{8}$

$=\frac{25+20+30}{168}=\frac{25}{56}$