Latest TCS Aptitude Question SOLUTION: There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at rand

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There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
a)1/2 b)14/19 c)37/38 d)3/4

Asked In TCS (13 years ago)

Solved Dr.Dipin Singh Read Solution (7)

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Read Solution (7) :

vamsi krishna reddy  (13 years ago)

the probability for selecting red box is 1/2 but randomly if we select green box, the probability will be 0.
so, total probability for this case is 0.5.

now consider the other case, 9 red balls are transferred to green ball box. now total balls in that box will be 19.

total probability = probability to select 1st box + probability to select 2nd box

= (1/2)*(1C1/1C1)+(1/2)*(9C1/19C1)

= (1/2)*(1+9/19)

= (1/2)*(28/19)

= 14/19

Is this solution Helpfull? Yes (81) | No (4)  

Dr.Dipin Singh  (13 years ago)

For the probability of getting a red ball is maximized, shift 9 red balls from one box to other box with 10 green balls.

Then prob of getting red ball will be

1*1/2 + (9/19)*(1/2) =1/2 +9/38 =28/38=14/19 .. option b.

Is this solution Helpfull? Yes (50) | No (2)  

X22  (12 years ago)

There is a formula:
x balls in first box and y balls in 2nd box.
x-1 balls are transferred to 2nd box. so total balls in 2nd box=y+x-1;
prob of selecting one box out of 2 is:1/2
maximum prob:
1/2*(1+(x-1)/(y+(x-1)))

Is this solution Helpfull? Yes (17) | No (7)  

mohsin  (8 years ago)

ek no. DIPIN bhai

Is this solution Helpfull? Yes (3) | No   

Swati  (7 years ago)

pls explain why 9 balls have been shifted

Is this solution Helpfull? Yes (3) | No   

hozefa  (8 years ago)

dipin bhai bhohot hard
mohsin bhai ek no

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

mohsin  (8 years ago)

@hozefa you are 1 no.

Is this solution Helpfull? Yes | No (2)  

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