Previous Problem List (/webwork2/wardSTAT2231F2 r kafando%40GoorgiaSouthern odus

Question

Previous Problem List (/webwork2/wardSTAT2231F2 r kafando%40GoorgiaSouthern oduskey Next (webwork2/wardSTAT223 IF 2017/ user leonel r kafando%40GeorgiaSouthern odu&effecti; euser leonel user leonel r kafando%40GeorgiaSouthern edu&offe; ctiveuser leonel r kafando%40Georgiasouthern eduskey (1 point) You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.8. With water it will die with probability 0.5. You are 86 % certain the neighbor will remember to water the plant When you are on vacation, find the probability that the plant will die Answer You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it? Answer Hint: it may heip to fii in a tabie like this one Plant lives Plant dies Total Neighbor remembers Neighbor forgets Total Note: You can ean partial credit on this problem. Preview My AnswersSubmit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor Page generated at 10/06/2017 at 02:30pm EDT WeBWork o 1996-2016 | theme: math4 I ww.version: 2.121 p9.version: 2.12] The WeBWorK Project (http/l/lwebwork.maa.org

Explanation / Answer

Question 1:

Using the law of total probability, probability that the plant will die is computed as:

P( die ) = P( water ) P( die | water ) + P( no water ) P( die | no water )

P( die ) = 0.86*0.5 + (1 - 0.86)*0.8 = 0.542

Therefore 0.542 is the required probability here.

Question 2:

Now given that the plant dead, probability that the neighbour forgots to water the plant is computed using the bayes theorem as:

P( no water | die ) = P( no water ) P( die | no water ) / P( die )

P( no water | die ) = (1 - 0.86)*0.8 / 0.542 = 0.2066

Therefore 0.2066 is the required probability here.

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