Question

You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.75. With water it will die with probability 0.4. You are 82 % certain the neighbor will remember to water the plant. You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it?

Answer 1

0.2915

Explanation:

Let W represent water and D represent Dying probability

W = water

D = die

->If with water, it will die with probability 0.4

P(W & D) = 0.82 x 0.4 = 0.328

->Without water the plant will die with probability 0.75

P(W ' & D) = 0.18 x 0.75 = 0.135

Taking sum of the above values with water and without water.

P(D) = P(W & D) + P(W ' & D) = 0.4643

P(W ' | D) = P(W ' & D) / P(D)

= 0.135 /0.463

= 0.2915 ≈ 29.15%

Thus, the probability the neighbor forgot to water is 0.2915