Question 1204883
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A bag contains {{{highlight(cross(of))}}} 45 markers of which 15 are pink. If you select 2 at random, 
without replacement, find the probability that:

a) Neither is pink.

b) At least one of the markers is pink.
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<pre>
(a)  The total number of all possible pairs is  {{{C[45]^2}}} = {{{(45*44)/2}}} = 990.

     
     If neither of randomly selected markers is pink, it means that all selected pairs are not pink.

     It means that they are from the set of 45-15 = 30 non-pink markers.

     The number of such pairs is  {{{C[30]^2}}} = {{{(30*29)/2}}} = 435.


     The probability "neither is pink" is the ratio  {{{P[(a)]}}} = {{{435/990}}} = {{{29/66}}}.    <U>ANSWER</U>



(b) This probability is the complement to the probability found in (a)

         {{{P[(b)]}}} = 1 - {{{P[(a)]}}} = 1 - {{{29/66}}} = {{{(66-29)/66}}} = {{{37/66}}}.    <U>ANSWER</U>
</pre>

Solved.


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Using complementary probability is very productive method for solving many similar problems.


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

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

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

in this site.