Question

Three ships $A,B$ and $C$ sail from England to India. If the ratio of their arriving safely are $2:5$, $3:7$ and $6:11$ respectively then the probability of all the ships for arriving safely is

• A. $\frac{18}{595}$
• B. $\frac{6}{17}$
• C. $\frac{3}{10}$
• D. $\frac{2}{7}$

Answer 1

The correct option is A

$\frac{18}{595}$

Explanation for the correct answer:

The ratio of ship $A$ arriving is $2:5$

Hence, the probability of ship $A$ arriving is given as

$p\left(A\right)=\frac{2}{2+5}=\frac{2}{7}$

The ratio of ship $B$ arriving is $3:7$

Hence, the probability of ship $B$ arriving is given as

$p\left(B\right)=\frac{3}{3+7}=\frac{3}{10}$

The ratio of ship $C$ arriving is $6:11$

Hence, the probability of ship $C$ arriving is given as

$p\left(C\right)=\frac{6}{6+11}=\frac{6}{17}$

The arrival of ships $A,B,C$ to India are independent events.

Hence, the probability of all three arriving is given as

$p\left(\mathrm{combined}\right)=p\left(A\right)\times p\left(B\right)\times p\left(C\right)$

$=\frac{2}{7}\times \frac{3}{10}\times \frac{6}{17}$

$\Rightarrow$ $p\left(\mathrm{combined}\right)=\frac{36}{1190}=\frac{18}{595}$

Hence, the probability of all three ships $A,B$ and $C$ arriving to India is $\frac{18}{595}$.

Hence, option A is the correct answer.