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

Algebra ->  Percentage-and-ratio-word-problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
.
A bag contains highlight%28cross%28of%29%29 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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(a)  The total number of all possible pairs is  C%5B45%5D%5E2 = %2845%2A44%29%2F2 = 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%5B30%5D%5E2 = %2830%2A29%29%2F2 = 435.


     The probability "neither is pink" is the ratio  P%5B%28a%29%5D = 435%2F990 = 29%2F66.    ANSWER



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

         P%5B%28b%29%5D = 1 - P%5B%28a%29%5D = 1 - 29%2F66 = %2866-29%29%2F66 = 37%2F66.    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.