The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching safely are \(2: 5,3: 7\) and \(6: 11\) respectively, then probability of all of them arriving safely is

The probability that ship ' \(A\) ' reaches safely is \(\mathrm{P}(\mathrm{A})=\frac{2}{2+5}=\frac{2}{7}\)
The probability that ship ' \(B\) ' reaches safely is \(\mathrm{P}(\mathrm{B})=\frac{3}{3+7}=\frac{3}{10}\)
The probability that ship ' \(\mathrm{C}\) ' reaches safely is \(\mathrm{P}(\mathrm{C})=\frac{6}{6+11}=\frac{6}{17}\)
\(\therefore \quad\) Probability that all of them arriving safely \(=\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})\) \(=\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{C})\)
[Since A, B, C are all independent events]
\(\begin{aligned}
& =\frac{2}{7} \times \frac{3}{10} \times \frac{6}{17} \\
& =\frac{18}{595}
\end{aligned}\)