Question

Let E be an event of a sample space S of an experiment, then P(S|E) =

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 :

The chances of P, Q and R getting selected as CEO of a company are in the ratio 4 : 1 : 2 respectively. The probabilities for the company to increase its profits from the previous year under the new CEO, P, Q or R are 0·3, 0·8 and 0·5 respectively. If the company increased the profits from the previous year, find the probability that it is due to the appointment of R as CEO.