Latest TCS Aptitude Question SOLUTION: . A drawer holds 4 red hats and 4 blue hats. what is probability of getting exactly 3 red hats or 3 blue hats when taking out 4 hats randomly out of drawer and immediately returnin

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

Asked In TCS Reddy (8 years ago)

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narendra  (8 years ago)

Probability to draw exactly 3 red hats and 1 blue hat is= 1/2*1/2*1/2*1/2=1/16
Probability to draw exactly 3 blue hats and 1 red hat is= 1/2*1/2*1/2*1/2=1/16
Total Probability= 1/16+1/16=1/8

Is this solution Helpfull? Yes (8) | No (1)  

abir  (8 years ago)

The possibilities...
3 red hats + 1 blue hat= 4C3 +4C1

SImilarly
3 blue hats + 1 red hat= 4C3 +4C1
therfore
porbablity = (4C3 *4C1)/8C4 + (4C3 *4C1)/8C4 =16/35

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

happy das  (8 years ago)

Probablity of taking out a particular color hat = 4/8 = 1/2

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

similary for (RRRB) = 4 * (1/2)4

answer = 8 * (1/2) ^4 = 1/2

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

Nikhil   (8 years ago)

2 choices for the first/second/third/fourth hat ==> Total number of possibilities : 2*2*2*2 = 16

4 ways to have 3 blue hats (BBBR, BBRB, BRBB, RBBB)

4 ways to have 3 red hats (RRRB, RRBR, RBRR, BRRR)

==> Answer is (4+4)/16 = 1/2

Is this solution Helpfull? Yes (2) | No   

taniya mukherjee  (8 years ago)

can you please explain the problem properly

Is this solution Helpfull? Yes (1) | No   

SARBASHIS KUNDU  (8 years ago)

Probability to draw exactly 3 red hats and 1 blue hat is= 1/2*1/2*1/2*1/2=1/16
Probability to draw exactly 3 blue hats and 1 red hat is= 1/2*1/2*1/2*1/2=1/16
(1/16*4)+(1/16*4) = 1/2
[here 4 is the combination of red & blue hats ]

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

vikas singh rajput  (8 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=1812×12×12=18
Similarly probability to draw 3 blue hats consecutively = 12×12×12=1812×12×12=18
Total probability = 12×12×12=1812×12×12=18+12×12×12=1812×12×12=18 = 14

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bhumika  (4 years ago)

Probability to draw exactly 3 red hats and 1 blue hat is= 8C3*8C1
Probability to draw exactly 3 blue hats and 1 red hat is=8C3*8C1
Total Probability= (4C3*4C1+4C3*4C1)/8C2

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krunal  (4 years ago)

RRRB + BBBR
= 4!/3! * (1/2*1/2*1/2*1/2*) + 4!/3! * (1/2*1/2*1/2*1/2*)
= 1/4 +1/4 =1/2

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