Question 1202128
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Trees planted by a landscaping firm have a 95% one-year survival rate. 
If they plant 16 trees in a park, what are the following probabilities?
(1) All the trees survive one year.
(2) At least 14 trees survive one year.
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        It is a binomial distribution probability problem.



<pre>
(1)    P = {{{0.95^16}}} = 0.4401  (rounded).    <U>ANSWER</U>



(2)    P(at least 14 survive one year) = P(16 survive) + P(15 survive) + P(14 survive) = 

     = {{{0.95^16}}} + {{{C[16]^15*0.95^15*(1-0.95)^1}}} + {{{C[16]^14*0.95^14*(1-0.95)^2}}} = 

     = {{{0.95^16}}} + {{{16*0.95^15*0.05}}} + {{{120*0.95^14*0.05^2}}} = 0.9571  (rounded).    <U>ANSWER</U>
</pre>

Solved.


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To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

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

in this site.


Learn the subject from there.