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14.Probability
medium
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
$\frac{2}{7}$
Solution
(a) We have ratio of the ships $A, B$ and $C$ for arriving safely are $2 : 5, 3 : 7$ and $6 : 11$ respectively.
$\therefore $ The probability of ship $A$ for arriving safely $ = \frac{2}{{2 + 5}} = \frac{2}{7}$
Similarly, for $B = \frac{3}{{3 + 7}} = \frac{3}{{10}}$ and
for $C$ = $\frac{6}{{6 + 11}} = \frac{6}{{17}}$
$\therefore $ Probability of all the ships for arriving safely
$= \frac{2}{7} \times \frac{3}{{10}} \times \frac{6}{{17}} = \frac{{18}}{{595}}$.
Standard 11
Mathematics
