First slide

Theorems of probability

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

Moderate

A

$\frac{18}{595}$
B

$\frac{6}{17}$
C

$\frac{3}{10}$
D

$\frac{2}{7}$

Solution

The ratios 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 is $\frac{2}{(2 + 5) - 217 .}$
Similarly, for B the probability is $\frac{3}{(3 + 7) = 3110}$ and for C the probability is $C = \frac{6}{(6 + 1 1) = 6 / 17 .}$
Therefore, the probability of all the ships for arriving safely is (2/7) x (3/10) x (6/17) = 18/595.

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