A gambler has in his pocket a fair coin and a two-headed coin. He withdraws a coin at random and
flips it twice. If the first flip is Heads, what is the probability that the second flip is Heads ?

• probability of finding head with fair coin=1/2*1/2=1/4.
  probability of finding head with unfair coin is 1/2*1=1/2.
  total probabilty of getting head=1/4+1/2=3/4.
• 12 years agoHelpfull: Yes(33) No(6)
• Sorry.... it will be...
  
  Probability of taking the FAIR coin AND probability of getting head is = 1/2 * 1/2 = 1/4
  Probability of taking the Unfair coin AND probability of getting head is 1/2 * 1
  The gambler can take the fair coin OR the unfair coin.
  Hence, The Answer 1/4 + 1/2 = 3/4
• 12 years agoHelpfull: Yes(17) No(2)
• @RAVI ....... if fair coin is chosen then how can we get this condition [ If the first flip is Heads, what is the probability that the second flip is Heads]
  because in fair coin there can,t be 2 heads
  so i think 3/4 is incorrect
• 12 years agoHelpfull: Yes(8) No(4)
• The second flip is completely an independent event. So....probability of getting is 1/2.
• 12 years agoHelpfull: Yes(2) No(5)
• taking a unfair coin and probability to get hed will be=1 because both side head
  takinh a fair coin then head =1/2
  so probability 1+1/2=3/2
• 12 years agoHelpfull: Yes(2) No(11)
• answer: 1/4
• 12 years agoHelpfull: Yes(1) No(9)
• u-event of taking unfair coin;h-event that head occurs;
  p(h)=3/4
  p(u AND h )=1/2
  THEREFORE,p(u|h)=p(u AND h)/p(h)=.5/.75=2/3.
  p(u|h)-probability that coin is unfair when head has occured
• 12 years agoHelpfull: Yes(1) No(6)
• show the proper method..
  
• 12 years agoHelpfull: Yes(0) No(2)
• If the coin is flipped twice the number of possibilities we get is 3 i.e HT, TH, HH
  where H(head),
  T(tail)
  If the fair coin is tossed then the possibity is {HT(first flip head 2nd flip tail), TH}
  IF the two headed coin is tossed the possibility is nly HH.
  Therefore on two counts head cms on the 2nd flip.. so as the possibities are 3,
  probabity ofgetting a head on 2nd flip is 2/3.
• 11 years agoHelpfull: Yes(0) No(0)
• there are 2 headed coins and 1 fair coin
  prob of choosing headed coin is 2/3 and of fair coin is 1/3
  here we have to see for second flip only.
  hence if headed coin is chosen then prob will be 2/3 x 1
  if fair coin chosen then prob will be 1/3 x 1/2
  total prob = 2/3 + 1/6 = 5/6
• 10 years agoHelpfull: Yes(0) No(0)
• sorry i thought there were 3 coins...
  1/2+1/2*1/2 = 3/4 ...
  correct answer
• 10 years agoHelpfull: Yes(0) No(0)
• According to me its 2/3 as in the first flip only its written that its head then on the second flip coins can be either headed or fair so total is 3 and for head the chances are only two that is from headed coin
• 9 years agoHelpfull: Yes(0) No(0)
• Fair coin gets chosen and 1st flip results in head and 2nd flip also results in head or two headed coin gets chosen and 1st flip is head and second flip is also head
  1/2*1/2*1/2+1/2*1*1=5/8
• 9 years agoHelpfull: Yes(0) No(0)
• probability of choosing fair coin =1/2
  choosing two-headed coin=1/2
  if fair coin selected probability of getting a H=1/2,T=1/2
  If two headed coin selected then probability og getting head=1
  so,in second flip probability of getting a head is possible in 3 ways
  For fair coin selection-->H H,T H
  for two headed coin --->H H
  so,(1/2*1/2*1/2)+(1/2*1/2*1/2)+(1/2*1*1)=1/8+1/8+1/2=6/8=3/4
• 9 years agoHelpfull: Yes(0) No(0)
• it is clearly mention that first flip is head,so we take care about only second flip
  if he is choosing fair coin it is definatly tail,and if two headed it is definatly head so probabily=1/2 only
• 9 years agoHelpfull: Yes(0) No(0)
• Total Case: {H,H,T}*{H,H,T}=HH,HH,HT,HH,HH,HT,TH,TH,TT
  So Probability= 6/8=3/4
• 9 years agoHelpfull: Yes(0) No(0)