Latest Elitmus Aptitude Question SOLUTION: Q.You have 3bags each containing two marbles.bag A contain 2 white marbles , bag B contaion 2 black marbles,bag C contains one white marble and one block marble. You pick a random

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Probability

Elitmus Question Papers:

(#M40141419) ELITMUS Numerical Ability question Probability Keep an EYE

Q.You have 3bags each containing two marbles.bag A contain 2 white marbles , bag B contaion 2 black marbles,bag C contains one white marble and one block marble. You pick a random bag and take out one marble.it is a white marble.probability that the remaining marble from the same bag is also white ?

Asked In Elitmus Rajul Singh Gaur (9 years ago)

Solved siddharth prakash singh Read Solution (15)

Is this Puzzle helpful?   (31)   (10) Submit Your Solution Probability

Read Solution (15) :

siddharth prakash singh  (9 years ago) Best Solution

probability to choose one bag= 1/3
now since it is given that first selected marble is white thus the selected bag must be either A or B.
now since we have to find the probability that the remaining marble from teh same bag is also white, hence the require bag is bag A.
so now there is only 1 favourable condition. hence req prob = (1/3)*1 = 1/3

correct me if um wrong.....

Is this solution Helpfull? Yes (32) | No (30)  

mayank  (9 years ago)

firstly... probability of choosing a RANDOM BAG= 1/3...

Then choosing a white marble from A Bag =2/2
similarly choosing a white marble from bag B=0/2
Then From bag C it is=1/2

So the probability=(1/3)*((2/2)+(0/2)+(1/2))
=(1/3)*((1+(1/2))
=(1/3)*(3/2)
=(1/2)

Is this solution Helpfull? Yes (31) | No (9)  

siddharth prakash singh  (9 years ago)

It is the problem of Conditional probability.
i.e. here it is given that the first picked marble is white. Hence total probability will not be equal to 1. As it will not include the case when fist marble in any case is black.
Our required condition is (w1w1) or(w2w2) or (w3w3)
now probability to choose any bag randomly =1/3
therefor favorable prob= 1/3[2/2*1/1) + 1/3[0] +1/3[1/2*0] =1/3
now total condition will be (w1w1 or w1b1) or (w2w2 or w2b2) or(w3w3 or w3b3)
=1/3[2/2*1/1 +2/2*0] + 1/3[0] + 1/3[1/2*0 +1/2*1/1] =1/3+1/6 =1/2
so the required probability= [ (w1w1) or(w2w2) or (w3w3) ] / [ (w1w1 or w1b1) or (w2w2 or w2b2) or(w3w3 or w3b3) ]
[1/3]/[1/2] = 2/3

Is this solution Helpfull? Yes (23) | No (4)  

Pritam  (9 years ago)

It is based on BAYES theorem.
Ans is 2/3

Is this solution Helpfull? Yes (10) | No (1)  

Abu  (9 years ago)

probability that the remaining marble from the same bag is also white = 1/2
remaining white marble may be either from bag A or bag C .

Is this solution Helpfull? Yes (9) | No (3)  

MR. X  (9 years ago)

probability of choosing any bag = 1/3

now, given first one is white
so,either it will be bag A or C.
so required probability

1/3*1 or(+) 1/3*(1/2)
=1/2.

correct me if um wrong.....

Is this solution Helpfull? Yes (9) | No (4)  

Abhishek  (7 years ago)

There are three bags , so selection of one of the bag is 1/3

white ball is in bag A and C

Now it is given in the question that 1 ball is drawn and it is white....so it is clear that ball should be drawn from Bag A

so Probability of again white ball is drawn from same bag is 1/3*(1/1 + 0/2+ 1/2) = 1/2

Is this solution Helpfull? Yes (2) | No (2)  

  (6 years ago)

Answer :
2
3
2/3

The bag selected is either bag A or bag C because first marble is white.

If Bag A is selected, first marble is white and hence second marble will be white.
If Bag C is selected, first marble is white and hence second marble will be black.

Therefore, second marble will be white only if the selected bag is A

Hence, probability that remaining marble from the same bag is white
= Probability of selecting Bag A

We know first marble is white. Bag A has two white marbles whereas bag C has only one white marble.
Therefore Probability of selecting Bag A =
2
3
2/3

=> Probability that remaining marble from the same bag is white = 2/3

Is this solution Helpfull? Yes (2) | No (1)  

vikash kumar anand  (9 years ago)

Here marbles not replaced and first one is white so probability of white marble in another two bag is equal to =2/5*1/4=2/20.

Is this solution Helpfull? Yes (1) | No (4)  

Arpit dubey  (8 years ago)

according to bayes theorem it is 2/3 but with ordinary aproach it becomes 1/2 .... can any one plz clarify?'

Is this solution Helpfull? Yes | No (3)  

santosh  (8 years ago)

bag can be A or C
1st is white so 2nd can be w/b so p =1/2

Is this solution Helpfull? Yes | No (3)  

saurabh kumar  (7 years ago)

1/3(1+0+1/2)=1/2

Is this solution Helpfull? Yes | No (2)  

Ayush Barnawal  (6 years ago)

check this out.. https://en.wikibooks.org/wiki/Puzzles/Statistical_puzzles/3_Bags_of_Marbles/Solution

Is this solution Helpfull? Yes | No   

dushyant kumar  (6 years ago)

Bag A=white,white
Bag B=black,black
Bag C=White, Black
So probability to choosing any one bag is 1/3.
But Only if we pick marbles either from bag A or Bag C then we can get a white marble
means that probability to choosing a white marble bag is 1/2.
And we all know that only Bag A have 2 white so probability is also 1/2 to getting another white.
hope u all understand...and correct me if i'm wrong

Is this solution Helpfull? Yes | No   

Kartik Choudhary  (5 years ago)

1/3*2/2*1/1+1/3*0/2+1/3*1/2*0/1==== 1/3 Ans.

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.