SOLUTION: A bag contains 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 mar

Question 1204883: A bag contains 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.
Answer by ikleyn(52832) (Show Source): You can put this solution on YOUR website!
.
A bag contains 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.
~~~~~~~~~~~~~~~~~~~~~~~~~~

(a)  The total number of all possible pairs is   =  = 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   =  = 435.


     The probability "neither is pink" is the ratio   =  = .    ANSWER



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

          = 1 -  = 1 -  =  = .    ANSWER

Solved.

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

To see many other similar (and different) solved problems of this type, look into the lessons
- Solving probability problems using complementary probability
- Solving probability problems using complementary probability REVISITED
in this site.

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