Aptitude - Probability - Discussion

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"Weakness of attitude becomes weakness of character."

- Albert Einstein

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

[A].

[B].

[C].

[D].

Answer: Option A

Explanation:

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then, n(S) = Number of ways of drawing 2 balls out of 7

= ⁷C₂ `

= (7 x 6)

(2 x 1)

= 21.

Let E = Event of drawing 2 balls, none of which is blue.

n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.

= ⁵C₂

= (5 x 4)

(2 x 1)

= 10.

P(E) = n(E) = 10 .

n(S) 21

Aarthi said: (Mon, Aug 16, 2010 11:09:23 AM)

Can we do this n different method? finding the possibility that both are blue and finally ans-1.

Soundar said: (Tue, Aug 24, 2010 01:37:04 AM)

Its a correct answer and short way.

Kk585 said: (Fri, Dec 24, 2010 07:04:51 AM)

Probability that the 2 balls r blue ----> 2c2/7c2 = 1/21 Probability that none of ball is blue ---> 1-(1/21) = 20/21 Why is my answer wrong please explain? p(a)+p(a(bar)) = 1 .......

Saurabh said: (Tue, Mar 22, 2011 12:32:07 AM)

This is the the simplest method to find the Probablity...........

Rose Were said: (Thu, May 19, 2011 04:10:10 AM)

Why are you multiplying by 6 and by 4?

Rose Were said: (Thu, May 19, 2011 05:58:22 AM)

How did the multiplications come about? please answer me.

Subhash said: (Fri, Jun 3, 2011 02:10:38 AM)

What Kk585 said is not correct. Becuase, here we should consider no ball is blue. pro.of 2 blue balls is (2c2/7c2), pro.of 1blue ball and another 1 green ball is((2c1/7c1)(3c1/6c1))2. Here 2 means b+g or g+b ways will occur. In the similar manner ,pro. of 1 b and 1 red is ((2c1/7c1)(2c1/6c1))2. Therefore total is 11/21. Hence ans is 1-(11/21) is 10/21.

Ekta said: (Mon, Aug 8, 2011 12:15:50 AM)

Please clarify it which one having best answer of the solution.

Akash said: (Mon, Sep 26, 2011 12:16:18 PM)

Can we do it by this way? 3c2+2c2+3c1 2c1 --------------- 7c2. I have done it this way. 3C2 means that the both balls would be green 2C2 both would be red and 3C1 and 2C1 because both the balls can be red and green. Isn't the solution correct?

Shiba said: (Tue, Sep 27, 2011 03:06:13 PM)

n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls. ? My question is why are you finding it only from 5 balls why not 7 balls.