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A bag contains $10$ blue marbles, $20$ green marbles and $30$ red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated $3$ times. The probability that no two of the marbles drawn have the same colour is

1. $\left(\dfrac{1}{36}\right)$
2. $\left(\dfrac{1}{6}\right)$
3. $\left(\dfrac{1}{4}\right)$
4. $\left(\dfrac{1}{3}\right)$

### 1 comment

Notice ->

Direct Hypergeometric distribution formula can not be applied because we are placing marbel back in the back.

No two marbles have the same color means, the final outcome of the three draws must be a permutation of

Blue, Green, Red

There are $3! = 6$ such permutations possible.

Now, probability of getting a Blue first, Green second and Red third $=\dfrac{10}{60}\times \dfrac{20}{60}\times \dfrac{30}{60}$

Required probability $=6\times \dfrac{10}{60}\times \dfrac{20}{60}\times \dfrac{30}{60} =\dfrac{1}{6}.$

Correct Answer: $B$
by

if we use (10C1 +20C2 + 30C2 ) / 60C2 is it ok ? in this one we have to mutilplay 3! or this formula give direct  right answer ?

formula is nCr

please guide me is it right or not ?
here in the question order of drawing a marble is not mentioned so we need to take the posibilities of orders so thats why we are multiplying with 3!
completely wrong , answer is 2/9

total combinations with three colors b,g,r is 27

favorable are 6 bgr,brg,rgb,rbg,grb,gbr

so 6/27=2/9
P (no two marble have the same colour) = 1 - P(Two or more marble have the same colour)

Case I --> P( Two marble same colour) = 3C2*P(both Red ,blue or Green) = 3*{(1/2*1/2*1/2)+(1/6*1/6*5/6)+(1/3*1/3*2/3)} ==> 24/36

Case II--> P(Three marble same colour) = 3C3*P(All Red, Blue or Green) = 1*{(1/2*1/2*1/2)+(1/3*1/3*1/3)+(1/6*1/6*1/6)} ==> 6/36

Therefore Probability of no two drawn marble have the same colour ==> { 1 - (30/36)} = 1/6 .
by

### 1 comment

You have arrived at correct answer. But for going from Delhi to Calcutta, instead of taking domestic flight you have taken international flight, flying over Atlantic and Pacific.
10/20 * 20/60 * 30/60 =1/6

what's wrong in it????plz explain
1/6 is correct. But calculation is wrong.