Latest TCS Aptitude Question SOLUTION: A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer a

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A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
A. 1/2
B. 1/8
C. 1/4
D. 3/8

Asked In TCS kanika (11 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

lala  (11 years ago)

When you take out hats one by one after replacement, there are equal chances of getting red or blue hat.

So possible outcomes are
RRRB, RRBR,RBRR,BRRR, BBBR,BBRB,BRBB,RBBB.. with exactly three red or blue hats.
RRBB,BBRR,RBRB,BRBR,BRRB,RBBR, BBBB,RRRR.. with other combinations.

so out of 16 possible combinations , eight are desired combinations.
so probability of getting exactly 3 red hats or exactly 3 blue hats when taking out 4 hats at random and return every hat to drawer before taking out another one = 8/16 =1/2

Is this solution Helpfull? Yes (55) | No (6)  

Mukta Yadav  (11 years ago)

There are 4 draws of the hats.
now for exactly 3 red hats, the possible draws are {R,R,R,B}; {R,B,R,R};{R,R,B,R};{B,R,R,R} i.e 4
similarly for exactly 4 blue hats,4 sets are possible, and
p(one red hat)=1/2 and p(one blue hat)=1/2
therefore as above sets: p(exactly 3 red hats)= [1/2)^4]*4
and p( exactly 3 blue hats) =[1/2)^4]*4
so, p(exactly 3 red hats or 3 blue hats) = p(exactly 3 red hats)+ p(exactly 3 blue hats) = 1/4+1/4 =1/2
therefore..ans..A. 1/2

Is this solution Helpfull? Yes (14) | No (4)  

Rahul mishra  (11 years ago)

i think ans is 1/4.....

Is this solution Helpfull? Yes (5) | No (14)  

shyam salona  (11 years ago)

total outcomes=2*2*2*2=16
expected outcomes=RBBB BRBB BBRB BBBR BRRR RBRR RRBR RRRB no=8
so p(N)=8/16=1/2

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

Sougata Sarkar  (11 years ago)

ans is 1/2

Is this solution Helpfull? Yes (2) | No (7)  

Alok Jain  (11 years ago)

4c1*4c1*4c1*4c1*4*2/(8c1*8c1*8c1*8c1)...

Is this solution Helpfull? Yes (2) | No   

sudhakar jain  (10 years ago)

One way to look at this problem is to count all the possible outcomes of 3 red plus 3 blue and dividing it by the total number of all color combinations
RRRB BBBR
RRBR BBRB
RBRR BRBB
BRRR RBBB which is a total of 8
For all possible color combinations, there are these (8) plus all red and all blue (2), two of each color (6) making a total of 16. The probability of getting 3 red or 3 blue is therefore 8/16 = 1/2

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

rajkumardubey  (11 years ago)

1/2.............

Is this solution Helpfull? Yes | No (3)  

riddhi soni  (11 years ago)

@ alok jain : i dint got y it is multiplied by 4, plz justify

Is this solution Helpfull? Yes | No (2)  

sumit kalra  (10 years ago)

As the objects are replaced, the probability of drawing red or blue is equal.
Probability to draw 3 red hats consecutively = 12×12×12=18
Similarly probability to draw 3 blue hats consecutively = 12×12×12=18
Total probability = 12×12×12=18+12×12×12=18 = 14

Is this solution Helpfull? Yes | No (6)  

Taniya  (9 years ago)

SHUBHAM SHANDILYA plz do calculate correctly

Is this solution Helpfull? Yes | No (4)  

SWAPNA ROY  (9 years ago)

As the objects are replaced, the probability of drawing red or blue is equal.
Probability to draw exactly 3 red hats and 1 blue hat = 12×12×12×12=116
Similarly probability to draw exactly 3 blue hats and 1 red hat = 12×12×12×12=116
Total probability = 116+116=18

Is this solution Helpfull? Yes | No (5)  

Akhilesh Kumar Shaw  (9 years ago)

As the objects are replaced, the probability of drawing red or blue is equal.
Probability to draw exactly 3 red hats and 1 blue hat = 12×12×12×12=116
Similarly probability to draw exactly 3 blue hats and 1 red hat = 12×12×12×12=116
Total probability = 116+116=18

Is this solution Helpfull? Yes | No (3)  

jithendra  (8 years ago)

((4^3).(4^1)+(4^3).(4^1))/(8^4)=(1/8)-------answer
(-----red------+------blue---)/(total outcomes) (; it is a replacement problem)
option B

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