Question

Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality totals. Previous records state that the probability of an airplane crash is 0·00001%. Further, there are 95% chances that there will be survivors after a plane crash. Assume that in case of no crash, all travellers survive. Let E₁ be the event that there is a plane crash and E₂ be the event that there is no crash. Let A be the event that passengers survive after the journey. On the basis of the above information, answer the following questions :

Let E and F be two events such that P(E) = 0·1, P(F) = 0·3, P(E ∪ F) = 0·4, then P(F|E) is :

If A and B are events such that P(A/B) = P(B/A) ≠ 0, then :

A departmental store sends bills to charge its customers once a month. Past experience shows that 70% of its customers pay their first month bill in time. The store also found that the customer who pays the bill in time has the probability of 0.8 of paying in time next month and the customer who doesn't pay in time has the probability of 0.4 of paying in time the next month.

Assertion (A) : If R and S are two events such that P(R | S) = 1 and P(S) > 0, then S ⊂ R. Reason (R) : If two events A and B are such that P(A ∩ B) = P(B), then A ⊂ B.