If unbiased coin is flipped 5 times ,the probability that same face does not show up in any 3 consecutive flips is:
A.1/2
B.5/8
C.3/8
D.7/8

• Calculate the compliment..HHHHH HHHHT HHHTT THHHT TTHHH THHHH TTTTTT TTTTH TTTHH HTTTH HHTTT HTTTT , ITS ANS IS 12 /32 = 3 / 8 NOW the req Ans is1-3/8=5/8
  
• 11 years agoHelpfull: Yes(11) No(12)
• Answer is A.1/2
  The probability of tossing one coin 5 times is same as tossing 5 coins at a time.
  Let assume first coin shows H(Head). See its decision tree below.
  
  -
  
  
  H
  H
  H
  T
  T
  H
  T
  _
  H
  _
  H
  T
  H
  H
  T
  T
  T
  H
  H
  T
  T
  
  _
  
  
  Total 8 outcomes.
  Similarly if first coin shows T(tail) then 8 outcomes.
  
  Total=16 outcomes.
  
  Total outcomes without any restriction= 2^5=32.
  
  So probability= 16/32=1/2
  
  
  
  
• 11 years agoHelpfull: Yes(7) No(4)
• Answer is A.1/2
  The probability of tossing one coin 5 times is same as tossing 5 coins at a time.
  Let assume first coin shows H(Head).
  The second coin can show HEAD or TAIL.
  so cases HEAD->HEAD
  HEAD->TAIL
  similarly, all possible cases when first coin shows head are
  1.HHTHH
  2.HHTHT
  3.HHTTH
  4.HTHHT
  5.HTHTH
  6.HTHTT
  7.HTTHH
  8.HTTHT
  
  Total 8 outcomes.
  Similarly u can do if first coin shows TAIL.
  Easy if create a rough decision tree.
  
  So if first coin shows T(tail) then 8 outcomes.
  
  Total=16 outcomes.
  
  Total outcomes without any restriction= 2^5=32.
  
  So probability= 16/32=1/2
  
  Hope it helps if anyone is having problem in understanding!
• 11 years agoHelpfull: Yes(5) No(0)
• Oops! Decision Tree is not shown in correct way here.
  
  See here the the favourable cases when first coin shows HEAD.
  1.HHTHH
  2.HHTHT
  3.HHTTH
  4.HTHHT
  5.HTHTH
  6.HTHTT
  
  Smilarly u can do if first coin shows TAIL.
  Easy if create a rough decision tree.
  7.HTTHH
  8.HTTHT
  
• 11 years agoHelpfull: Yes(4) No(1)
• For faster calculations:-
  Write the set corresponding to three coins and two coins.
  {HHH,HTH,THH,TTH,HHT,HTT,THT,TTT} x{HH,HT,TH,TT}
  Now, make set in mind and check for each formed combinations and count the nuuber of possible outcomes which does not have 3 consecutive same face. it will give total of 16 possible outcomes and hence probalilty is 1/2
• 11 years agoHelpfull: Yes(3) No(0)
• at least 3 consecutive heads there are 8 cases
  HHHHH
  HHHHT
  HHHTH
  HHHTT
  TTHHH
  THHHH
  HTHHH
  THHHT
  at leat 3 consecutive tail,there are also 8 cases
  p=(8+8)/2^5=1/2 (ans)[2^5 is total outcome]
• 11 years agoHelpfull: Yes(2) No(2)
• ans=7/8
  ways in which 3 consecutive flip comes..
  hhhhh
  hhhtt
  tthhh
  hhhht
  thhhh
  thhht
  hhhth
  hthhh
  total occurance=2^5=32
  probability for same face occuranc=8/32
  probability that same face wont occur=1-8/32=7/8
• 11 years agoHelpfull: Yes(2) No(1)
• answer=0.25
  required probability=1-(24/2^5)
• 11 years agoHelpfull: Yes(1) No(3)
• could any one of you explain clearly plz....
• 11 years agoHelpfull: Yes(1) No(1)
• case 1:take 3 heads as 1 unit and onter 2 coins as tail so they can be arranged
  in 3!=6 ways:
  case 2:take 4 heads as 1 unit and other tail so they can be arranged in 2!=2 ways
  case 3:5 heads in 1 way
  thus,total ways where 3 heads appear consecutively=6+2+1=9
  similarly there are 9 ways where tail appear consecutively
  thus,total=18
  probability of appearing consecutively(p)=18/32
  thus,q=1-p=1-18/32=7/8(ans)...
• 11 years agoHelpfull: Yes(1) No(0)