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If a parachutist lands at a random point on a line between markers A and B, find the probability that she is closer to A than to B.

Find the probability that her distance to A is more than seven times her distance to B.

Answer 1

Probability that she is closer to A than to B is computed here as:
Let the middle point of AB be C. Therefore we get here: AC = BC

Then, she is closer to A than to B, when we are in the range AC and not in BC.

Therefore the probability here is computed as:
= AC/AB = 1/2

Therefore 0.5 is the required probability here.

Now probability that her distance to A is more than 7 times her distance to B is computed here as:

Let us divide the line AB into 8 equal parts:

Ac₁ = c₁c₂ = c₂c₃ = c₃c₄ = c₄c₅ = c₅c₆ = c₆c₇ = c₇B

Therefore, we have here:
Ac₇ = 7c₇B

Therefore the distance from A would be more than 7 times her distance from B when she would lie in c₇B

Therefore the required probability here is computed as:
= c₇B/AB
= 1/8

Therefore 1/8 = 0.125 is the required probability here.