Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the probability that the exactly two ships arrive safely is

Step-by-step solution

Let P(A) , P(B) , and P(C) be the probabilities of safe arrival for ships A, B, and C respectively. Given the odds in favour of their safe arrival, we can find their probabilities: P(A) = 2 2+5 = 2 7 P( A ) = 1 - 2 7 = 5 7 P(B) = 3 3+7 = 3 10 P( B ) = 1 - 3 10 = 7 10 P(C) = 6 6+11 = 6 17 P( C ) = 1 - 6 17 = 11 17 The probability that exactly two ships arrive safely is the sum of the probabilities of three mutually exclusive cases: A and B arrive but C does not, A and C arrive but B does not, and B and C arrive but