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

• 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
  
• 12 years agoHelpfull: Yes(55) No(6)
• 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
• 12 years agoHelpfull: Yes(14) No(4)
• i think ans is 1/4.....
• 12 years agoHelpfull: Yes(5) No(14)
• 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
• 12 years agoHelpfull: Yes(3) No(3)
• ans is 1/2
• 12 years agoHelpfull: Yes(2) No(7)
• 4c1*4c1*4c1*4c1*4*2/(8c1*8c1*8c1*8c1)...
• 12 years agoHelpfull: Yes(2) No(0)
• 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
• 11 years agoHelpfull: Yes(1) No(2)
• 1/2.............
  
• 12 years agoHelpfull: Yes(0) No(3)
• @ alok jain : i dint got y it is multiplied by 4, plz justify
• 12 years agoHelpfull: Yes(0) No(2)
• 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
• 11 years agoHelpfull: Yes(0) No(6)
• SHUBHAM SHANDILYA plz do calculate correctly
• 10 years agoHelpfull: Yes(0) No(4)
• 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
• 10 years agoHelpfull: Yes(0) No(5)
• 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
• 9 years agoHelpfull: Yes(0) No(3)
• ((4^3).(4^1)+(4^3).(4^1))/(8^4)=(1/8)-------answer
  (-----red------+------blue---)/(total outcomes) (; it is a replacement problem)
  option B
• 9 years agoHelpfull: Yes(0) No(0)