The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching…
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
$\frac{18}{595}$
$\frac{11}{34}$
$\frac{196}{217}$
$\frac{1}{595}$
Solution
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]
$\begin{aligned}
& =\frac{2}{7} \times \frac{3}{10} \times \frac{6}{17} \\
& =\frac{18}{595}
\end{aligned}$