Question 1183576
.
When Tanawat goes on holiday, he asks his friend Niran to water his
plant for him while he is away.
If Niran does not water the plant correctly, the probability that the plant will die is 0.8.
If Niran does water the plant correctly, there is still a probability of 0.2 that it will die.
The probability that Niran will water the plant correctly is 0.7.

a) Use a tree diagram to work out the probability that the plant will be alive when Tanawat returns.

b) What is the probability that Niran did not water the plant properly, given that Tanawat returns to find that his plant is dead?
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<pre>
(a)  P(alive) = 0.7*(1-0.2) + (1-0.7)*(1-0.8) = 0.62.    <U>ANSWER</U>



(b)  P(dead) = 0.7*0.2 + (1-0.7)*0.8 = 0.38   (by the way, it is the complementary probability to the obtained in part (a) ).

     
     P(under question b) is the conditional probability = the ratio of


         P(Niran did not water the plant AND the plant is dead)  to  P(dead) = 


           = {{{((1-0.7)*0.8)/(0.7*0.2 + (1-0.7)*0.8)}}} = {{{(0.3*0.8)/0.38}}} = {{{0.24/0.38}}} = {{{12/19}}} = 0.6316.    <U>ANSWER</U>
</pre>

Solved.


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On conditional probability, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-conditional-probability-problems.lesson>Conditional probability problems REVISITED</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-problems-on-Conditional-probability.lesson>More problems on Conditional probability</A> 

in this site.


Read them to develop your skills and knowledge.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>" 
and &nbsp;"<U>Additional problems on Probability</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.