Please provide the work / details for the solutions to problems A and B. Thank Y

Question

Please provide the work / details for the solutions to problems A and B. Thank You

You ask your neighbor to water a sickly plant while you are on vacation. Without water, it will die with probability .8: with water, it will die with probability.15. You are 90 percent certain that your neighbor will remember to water the plant. (a) What is the probability that the plant will be alive when you return? (b) If the plant is dead upon your return, what is the probability that your neighbor forgot to water it?

Explanation / Answer

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P( dead w/0 water) = .8
P( dead with water) = .15

P( neighbor will water the plants ) = .90
P( neighbor will not water the plants ) = 1-P( neighbor will water the plants ) = 1-.90 = .10

a. P( plant will be alive when you return) = P( neighbor will water the plants )*P(not dead with water after neighbor waters) + P( neigbor will not water the plants)*P(not dead with water even after neighbor doesn't water)

= 0.9*(1-.15)+(1-.9)*(1-.8) = .785

b. P( given plant is dead, chances that neighbor forgot to water) = ?
= P(neighbor forgot to water and the plant' dead) / P( plant is dead)
= ( 1-.9)*(.8)/ (( 1-.9)*(.8) + (.9)(.15))
= .3721

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