Question

A problem in mathematics is given to three students whose chances of solving it are $\frac{1}{3},\frac{2}{7},and\frac{3}{8}$ respectively What is the probability that the problem will be solved?

Answer 1

Let $A,B,C$ be the respective events of solving the

problem and $\overline{A},\overline{B},\overline{C}$ the respective events of not

solving the problem.Then $A,B,C$ are independent events

$\therefore \overline{A},\overline{B},\overline{C}$ are independent events

Now $P\left(A\right)=1/3$ $P\left(\overline{A}\right)=1-1/3=2/3$

$P\left(B\right)=2/3$ $P\left(\overline{B}\right)=1-2/7=5/7$

$P\left(C\right)=3/8$ $P\left(\overline{C}\right)=1-3/8=5/8$

$\therefore$ P (none solves the problem

$=P(no+A)\times P(no+B)\times P(no+B)$

$=\frac{2}{3}\times \frac{5}{7}\times \frac{5}{8}=\frac{50}{168}$

Hence , $P$ ( the problem will be solved )

$=1-P$ (None solves the problem

$=1-\frac{50}{168}=\frac{118}{168}=\frac{59}{84}$