SOLUTION: A bag contains three red, four white and three black, identical balls, three balls are drawn at random without replacement from the bag. What is the probability that at

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Question 1163284: A bag contains three red, four white and three black, identical balls, three balls are drawn at random without replacement from the bag. What is the probability that at least a ball is white.
Found 2 solutions by dkppathak, ikleyn:
Answer by dkppathak(439)   (Show Source): You can put this solution on YOUR website!
A bag contains three red, four white and three black, identical balls, three balls are drawn at random without replacement from the bag. What is the probability that at least a ball is white.
solution
total balls =3+4+3=10 and white balls are 4
probability of at least one white = probability of 1 white + probability of two white + probability of three white
=4c1x6c2/10c3+4c2x6c1/10c3+4c3x6c0/10c3
4x15/120+6x6/120+4x1/120
60/120+36/120+4/120
100/120
=20/24=5/6
Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
A bag contains three red, four white and three black, identical balls, three balls are drawn at random
without replacement from the bag. What is the probability that at least one ball is white.
~~~~~~~~~~~~~~~ 

The total balls is  3 + 4 + 3 = 10.


The probability that at least one ball of the three drawn is white is the COMPLEMENT to the probability

that NO ONE of THE THREE BALLS is white.


In this complementary situation, you select every time from the set of red and black balls, whose total number initially is 3 + 3 = 6.


This complementary probability is  P' =  =  =  =  = .


So, the answer to the problem's question is


    P = 1 - P' = 1 -  = .

Solved.

Using complementary probability makes the solution much easier.

Actually, using complementary probability is a STANDARD method solving such problems.

------------

To see many other similar problems, solved in this way, see the lesson
    - Solving probability problems using complementary probability
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Solved problems on Probability".


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.

Consider this lesson as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.

Happy learning (!)


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