Question

You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.7. With water it will die with probability 0.45. You are 83 % 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

0.2416

Explanation:

P(forgot to water | dead) = P(forgot and dead) / P(dead)

->With water it will die with probability 0.45

P(watered and dead) =0.83 x 0.45 = 0.3735

->Without water the plant will die with probability 0.7

P(forgot and dead) = (1-0.83) x 0.7 => 0.17 x 0.7 =>0.119

P(dead) = P(watered and dead) +P(forgot and dead)

P(dead) = 0.3735 + 0.119= 0.4925

P(forgot to water | dead) =0.119 / 0.4925= 0.2416

Therefore, the probability the neighbor forgot to water the plant is 0.2416