Latest TCS Aptitude Question SOLUTION: A drawer holds 4 red hats and 4 blue hats. wt is probability of getting exactly 3 red hats or 3 blue hats when taking out 4 hats randomly out of drawer and immediatly returning eve

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A drawer holds 4 red hats and 4 blue hats. wt is probability of getting exactly 3 red hats or 3 blue hats when taking out 4 hats randomly out of drawer and immediatly returning every hat to drawer b4 taking out next??

Asked In TCS sahana (10 years ago)

Solved Aditya Read Solution (17)

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Aditya  (10 years ago)

ans:1/2
probability of getting exactly a red or blue hat = 4/8 =1/2
Probability of getting exactly three red:
P(RRRB)=(1/2)^4
P(RRBR)=(1/2)^4
P(RBRR)=(1/2)^4
P(BRRR)=(1/2)^4
total=4(1/2)^4
similarly for exactly 3 blue:
P(BBBR)=(1/2)^4
P(BBRB)=(1/2)^4
P(BRBB)=(1/2)^4
P(RBBB)=(1/2)^4
total=4(1/2)^4
total probability=4(1/2)^4+4(1/2)^4
=>1/4+1/4=1/2

Is this solution Helpfull? Yes (27) | No (11)  

ankit chauhan  (10 years ago)

4c3*4c1+4c3*4c1/8c4=32/70

Is this solution Helpfull? Yes (22) | No (6)  

Pooja Udayan  (10 years ago)

ans is 1/8.
as the hats are being replaced each time .so whenever we are taking out the hats we have same no. of hats in the drawer. therefore each time we have the probability of 4/8.
thus total 4 hats are taken out so (4/8*4/8*4/8*4/8)*2
*2 as 2 cases are considered
=1/8 ans

Is this solution Helpfull? Yes (20) | No (6)  

Arun  (10 years ago)

Ans: ((4C3*4C1)*2)/8C4
which is equal to 16/35...

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

Karthika  (10 years ago)

Guys,compare this question with flipping a coin.
Suppose exactly 3 heads or 3 tails are to be obtained when the coin is flipped 4 times.
So chances for exactly 3 heads are {HHHT,HHTH,HTHH,THHH}.
and chances for exactly 3 tails are {TTTH,TTHT,THTT,HTTT}.
We know when a coin is flipped 4 times,16 cases are obtained.
hence probability of getting exactly 3 heads= 4/16
and similarly probability of getting 3 tails is 4/16
our question is probability of getting exactly 3 heads or probability of getting 3 tails = 4/16 + 4/16 =1/2
So the coin logic can be used to solve the above hat problem.
our question is probability of getting exactly 3 red hats or probability of getting 3 blue hats(out of picking 4 hats randomly) = 4/16 + 4/16 =1/2

Is this solution Helpfull? Yes (11) | No (1)  

ANKUR SINGH  (10 years ago)

to select exactly 3 red hats n 1 blue hat = (4C3.4C1)
to select 4 hats from 8 hats = 8C4
to select exactly 3 blue hats n 1 red hat = (4C3.4C1)
to select 4 hats from 8 hats = 8C4
so total probability = (4C3.4C1)/8C4 + (4C3.4C1)/8C4 = 2(4C3.4C1)/8C4

Is this solution Helpfull? Yes (5) | No (6)  

SAGAR DAS  (10 years ago)

probability of finding one red hat=4/8
& probability of finding one blue hat =4/8.
since there is replacement factor..so total prob
is=((4/8)^4)+((4/8)^4)=1/8...ans

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Pooja Udayan  (10 years ago)

@karthika...see we have to take out a total of 4 hats so every time we have 8 hats in the drawer out of which we have to take out 4. so 4/8
thus for 3 red hats + 1 blue hat we have probability (4c1/8c1)*(4c1/8c1)*(4c1/8c1)*(4c1/8c1)
thus 2nd case for 3 blue hats and 1 red hat.so multiply by 2 at the end ...thus 1/8 comes the answer.

Is this solution Helpfull? Yes (3) | No (2)  

Amisha Agarwal  (10 years ago)

ans:1/4
p(R)=(4/8)^3=1/8
P(B)=(4/8)^3=1/8
so,p=1/8+/8=1/4

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

aditi patel  (10 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

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Prakash Singh  (10 years ago)

(1/2)*(1/2)*(1/2)*2

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Karthika  (10 years ago)

@ Pooja.. I couldn't understand the logic..i mean the 4/8 probability used,and replacement yu have mentioned.. I saw the answer as 1/8 in some other sites. Can yu please explain it in detail.. am confused if the answer is 1/8 or 3/8

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arvind  (10 years ago)

the way of choosing 1 red hat is=4 and
the way of choosing 1 blue hat is=4
so the comb. of 3 red in 4 hats is=
red,red,red,blue this can be happen with 4 ways so total ways =
4*4*4*4*4
similarly for 3 blue in 4 hats=
4*4*4*4*4
and total ways to take out 4 hats=8*8*8*8
hence the prob=favorable/total :=2*(4^5)/8^4 == 1/2

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nikhil pande  (10 years ago)

2*4c3*4c1/8c4

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Rohit kumar prasad  (10 years ago)

Now assume we have 2 take 3 blues and 1 red

P(BBBR) = (1/2)^4
P(BBRB) = (1/2)^4
P(BRBB) = (1/2)^4
P(RBBB) = (1/2)^4
total = 4 * (1/2)^4

similarly with red

thus the total is 2*4*1/16 = 8/16 = 1/2

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Neha Sharma  (8 years ago)

Correct Answer is 1/8...100% sure..
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 = 1/2×1/2×1/2×1/2=1/16
Similarly probability to draw exactly 3 blue hats and 1 red hat = 1/2×1/2×1/2×1/2=1/16
Total probability = 1/16+1/16=1/8

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v.lavanya  (8 years ago)

4c1/8*4c1/8*4c1/8+4c1/8*4c1/8*4c1/8=1/2

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