The probabilities that a man makes a certain dangerous journey by car, motor cycle or on foot are 1 / 2,1 / 6 and 1 / 3 respectively. The probabilities of an accident when he uses these means of transport are 1 / 5,2 / 5 and 1 / 10 respectively. Which of the following statement(s) hold good?

Step-by-step solution

aligned & B ₁= Journey by car & B ₂= Journey by motor cycle & B ₃= Journey on foot aligned aligned & P (B₁ )= 1 2 & P (B₂ )= 1 6 & P (B₃ )= 1 3 aligned Let A = accident occurs aligned & P ( ~A / B ₁ )= 1 5 ; P ( ~A / B ₂ )= 2 5 ; P ( ~A / B ₃ )= 1 10 & P ( ~A )= P ( ~A ~B ₁ )+ P ( ~A ~B ₂ )+ P ( ~A ~B ₃ ) & = P ( ~B ₁ ) P ( ~A / B ₁ )+ P ( ~B ₂ ) P ( ~A / B ₂ ) & + P ( ~B ₃ ) P ( ~A / B ₃ ) & = 1 2 1 5 + 1 6 2 5 + 1 3 1 10 & = 3 30 + 2 30 + 1 30 = 6 30 = 1 5 aligned (A) is correct P ( ~B ₁ / A )= 1 2 1 5 1 5 = 1 10