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 0.4. You are 86 % certain the neighbor will remember to water the plant.

Probability (plant surviving with water) = 0.516 Probability (plant surviving without water) = 0.042 Total probability (plant surviving) = 0.558 Probability (Plant dying with water) = 0.344 Probability (plant dying without water) = 0.098 Total probability (plant dying) = 0.442

Step-by-step explanation:

Pr (Neighbour waters) = 86% = 0.86

Pr (Neighbour doesn't water) = 1 - [ Pr (Waters) ] = 1 - 0.86 = 0.14

Pr (Plant dies with water) = 0.4

Pr (Plant survives with water) = 1 - [Pr (plant dies with water) ] = 1 - 0.4 = 0.6

Pr (Plant dies without water) = 0.7

Pr (Plant survives without water) = 1 - [Pr (plant dies without water) ] = 1 - 0.7 = 0.3

1. Probability of Plant Surviving:

A. With Water = Pr [with Water & survives ] = (0.86 x 0.6) = 0.516

B. Without Water = Pr [without water & survives] = (0.14 x 0.3) = 0.042

C. Plant Survived = Pr [ (with Water & survives) or (without water & survives) ]

0.516 + 0.042 = 0.558

2. Probability of plant Death:

A. With Water = Pr [with Water & dies ] = 0.86 x 0.4 = 0.344

B. Without Water = Pr [ Without Water & dies] = 0.14 x 0.7 = 0.098

C. Plant dies = Pr [ (with Water & dies) or (without water & dies) ]

= 0.344 + 0.098 = 0.442

Step-by-step explanation:

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 0.4. You are 86 % certain the neighbor will remember to water the plant.

Prob for plant dying with water = prob that he waters but plant dies

= 0.86*0.4

= 0.344

Prob for plant dying without water = prob that he does not water and the plant dies

= (1-0.86) * 0.7

= 0.098