4 A parachutist lands at random point on a line between mark

4. A parachutist lands at random point on a line between markers A and B. a) Find the probability that she is closer to point A than 13. b) Find the probability that her distance to A is more than three times her distance to B.

Solution

4a. The parachutist land closer to A than B or to B than A with equal probability since A and B are unbiased, and must add up to 1. Hence the required probabilty is 1/2.

b. Consider a point C in between A and B such that C is at a distance x from B and 3x from A. Such a point can always be found as we just need to divide the line into 4 equal parts. Since the parachutist has to land in the segment AC, required probability = (length of AC)/(length of AB) = 3/4