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 and

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(#M40010646) TCS Numerical Ability question Keep an EYE

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 immediatly returning every hat to the drawer before taking out the next?
a)1/2
b)3/8
c)1/4
d)1/8

Asked In TCS reema sharma (11 years ago)

Unsolved Read Solution (26)

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Read Solution (26) :

nagarjun  (11 years ago)

4 red,4 blue (asked exactly 3r or 3b)
probability for drawing red hat is 4/8 note: he returning every hat to drawer
firstly exactly 3 red is= 4/8*4/8*4/8*(4/8)=1/16
exactly 3 blue= 4/8*4/8*4/8*(4/8)=1/16
OR =1/16+1/16=1/8

Is this solution Helpfull? Yes (165) | No (59)  

supali  (11 years ago)

The order is also important here. RRRB or BBBR.
RRRB has 4 possible arrangements and BBBR too. So a total of 8 arrangements. For each of these arrangements p=1/16 so
Ans = 8/16 = 1/2

Is this solution Helpfull? Yes (55) | No (67)  

nagarjun  (11 years ago)

yes i forgot the combinations ,thanks
4 red,4 blue (asked exactly 3r or 3b)
probability of taking red hat is=4(red hats)/8(total)// for all probabilites will be same in this problem
exactly 3 red =4C3
exactly 3 blue=4c3
probability for drawing red hat is 4/8 note: he returning every hat to drawer
firstly exactly 3 red is= 4C1{4/8*4/8*4/8*(4/8)}=1/4
exactly 3 blue= 4C1{4/8*4/8*4/8*(4/8)}=1/4
OR =1/4+1/4=1/2

Is this solution Helpfull? Yes (36) | No (38)  

Santosh Kumar M S  (11 years ago)

4 red,4 blue (asked exactly 3r or 3b)
probability for drawing red hat is 4/8 note: he returning every hat to drawer
firstly exactly 3 red is= 4/8*4/8*4/8*(4/8)=1/16
exactly 3 blue= 4/8*4/8*4/8*(4/8)=1/16
OR =1/16+1/16=1/8
hey this correct ans

Is this solution Helpfull? Yes (29) | No (22)  

Shubham Shandilya  (10 years ago)

4c3*4c1/8c4=1/8

Is this solution Helpfull? Yes (19) | No (16)  

Anshul Gupta  (11 years ago)

we need RRRB or BBBR for exact three red and blue hats. and in first case (RRRB)
we get these 3 R in one case by probability
(4c1/8c1)(R)*(4c1/8c1)(R)*(4c1/8c1)(R)*(4c1/8c1)(B)=(4c1/8c1)^4
and we have 4 cases for exactly 3 R :(RRRB)(RRBR)(RBRRR)(BRRR)
SO THE PROB FOR EXACTLY 3 R IS 4*((4c1/8c1)^4)
similarly for 3 blue is 4*((4c1/8c1)^4)
and for both cases 4*((4c1/8c1)^4)+4*((4c1/8c1)^4) =1/2
ans. 1/2

Is this solution Helpfull? Yes (15) | No (18)  

Neena Thommy  (11 years ago)

notice that here we have to take rrrb or bbbr
case 1: rrrb
in dis we can take first "r" den return it .hence for "rrr" we hav probability 1/2.aftr that "b" can take.all the hats are der.and probabilty to take "b" is also 1/2.
so for take rrrb we have 1/2*1/2=1/4
similarly case2:bbbr is 1/2*1/2=1/4

hence 1/4+1/4=2/4=1/2

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

Karthikeyan  (9 years ago)

Option (2) Correct
pos s i bl e out comes=
(RRRR)(RRRB)(RRBR)(RBRR)(BRRR)(BBBR)(BBRB)(BRBB)(RBBB)(RRBB)(BBRR)(RBBR)(BRRB)(RBRB)(BRBR)(BBBB)
s o t ot al 16
n we want exact l y 3 bl ue hat s
s o 4/16=1/4 ans .

Is this solution Helpfull? Yes (9) | No (5)  

reema sharma  (11 years ago)

@NAGARJUN..
correct ansr is 1/2.can u plz elaborate ur ansr more..

Is this solution Helpfull? Yes (4) | No (8)  

deena  (9 years ago)

first of all find the n(S) which is taking 4 hats randomly out 0f 8.its mentioned that we should return the hat we took before taking next hat so n(s)=8c1*8c1*8c1*8c1=8*8*8*8.then find the n(a) which is getting exactly 3 red hats that means 3 red and one blue hats. n(a)=4c1*4c1*4c1*(4c1)=4*4*4*4.therefore p(A)=n(a)/n(s)=4*4*4*4/8*8*8*8=1/16.Similarly p(b)=n(b)/n(s)=(4)*(4)*(4)*4/8*8*8*8=1/16.OR=1/16+1/16=2/16=1/8.

Is this solution Helpfull? Yes (4) | No (2)  

tushar ghude  (10 years ago)

read it carefully you want either red or blue. answer seems to be 1/8 but "actually its 1/4" there are 4 red and 4 blue and u immediately return hat before taking out next so
probability of getting red = probability of getting blue = 4/8 = 1/2
now lets begin... I picked one hat. for the 1st pick color doesn't matter (i want either three red or three blue hats remember?) lets say i picked red now i returned it now i want two more red hats there are 4 red out of 8 probability of getting red is now 1/2
in short,
probability of getting any(red/blue) color * probability of getting same color * probability of getting same color again is (probability of getting any color is 1 always)
1* 1/2 * 1/2 = 1/4 is the correct answer.

Is this solution Helpfull? Yes (3) | No (8)  

anusha  (9 years ago)

Ans) 1/8
Probability that exactly 3 red hats out of four : 1/2*1/2*1/2*1/2 (Return every hat)
Probability that exactly 3 blue hats out of four : 1/2*1/2*1/2*1/2
1/16+1/16=2/16 =>1/8

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

Arijit Bhattacharya  (8 years ago)

DIVYA how can probability be greater than 1?

Is this solution Helpfull? Yes (2) | No   

ARCHIKA NAAG  (8 years ago)

they never asked for order to be RRRB OR BBBR..So ans should be 1/8

Is this solution Helpfull? Yes (2) | No   

Lovejeet Singh  (11 years ago)

Please Explain properly......!!!!
Answer is right.... but how we get is still a mystery for me !!!!

@supali: how we get p=1/16 ??

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

disha verma  (11 years ago)

i am not able to understand..plz elaborate it..

Is this solution Helpfull? Yes (1) | No (5)  

koushik bhakat  (9 years ago)

1/2 is the correct answer

Is this solution Helpfull? Yes (1) | No (3)  

Pratap Bhunia  (8 years ago)

the answer is a) 1/2

Is this solution Helpfull? Yes (1) | No (5)  

ria  (8 years ago)

we have to take out exactly 3 red hat or three blue hat so our combination are 4c3*4c1 for red color hats and 1 blue color hat and again 4c1*4c3 for red and blue color hats..... and probability is not more than 1 ...so our solution is..

(1/2*2*4c3*4c1)/8c4= 1/8 is the right answer.

Is this solution Helpfull? Yes (1) | No   

dinesh a  (7 years ago)

8C4=70

4C3=4 since two types of hats are there 4+4=8

probability = 8/70 approx 1/8.7 but not confrim :(

so 1/8

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

Riya malaiya  (6 years ago)

ans : 1/2
total possible outcomes are = RRRR RRRB RRBR RRBB RBRR RBRB RBBR RBBB BRRR BRRB BRBR BRBB BBRR BBRB BBBR BBBB
probablitiy of getting exactly 3 red hats = 4/16
3 blue hats = 4/16
both= 4/16+4/16 = 1/2

Is this solution Helpfull? Yes (1) | No   

Tridib Samanta  (4 years ago)

Total number of hats = 8
We can select one hat from 8 hats in 8c1 ways.

Total red hats = 4
We can select one red hat from 4 red hats in 4c1 ways.

Total blue hats = 4
We can select one blue hat from 4 blue hats in 4c1 ways.

Probability of selecting 3 red hats
4c1/8c1 x 4c1/8c1 x 4c1/8c1 = 1/8

Probability of selecting 3 blue hats
4c1/8c1 x 4c1/8c1 x 4c1/8c1 = 1/8

Add both of them (as OR is mentioned in question) -
1/8 + 1/8 = 1/4

Answer : 1/4

Is this solution Helpfull? Yes (1) | No   

mani  (8 years ago)

ans is 1/4

Is this solution Helpfull? Yes | No (1)  

divya  (8 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 (4)  

Lakshmi  (4 years ago)

with replacement
3 red hats can be possible in 4/8*4/8*4/8*4/8=1/16
similarly 3 blue hats is 1/ 16
therefore 1/16+1/16
=2/16
=1/8

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Lakshmi  (4 years ago)

with replacement
3 red hats can be possible in 4/8*4/8*4/8*4/8=1/16
similarly 3 blue hats is 1/ 16
therefore 1/16+1/16
=2/16
=1/8

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