a person draws a card from a pack of 52,replaces it and shuffle it.he continues doing so untill he draws a heart..what is the probability that he has to make at least 3 trials?

• Sorry
  
  make 3 trials before drawing out a heart.
  So, in the first two trials he must draw anything else but not the heart.
  Probability of choosing any other card except the heart: 39/52 = 3/4
  Probability of drawing a heart: 13/52 = 1/4
  
  draw any two cards except the heart for the first two.
  So, prob = (3/4)*(3/4) = 9/16
  He has to draw a heart in the third trial.
  So, total prob = (9/16)*(1/4) = 9/64
• 10 years agoHelpfull: Yes(52) No(15)
• HEY GUYS I GOT THE ANSWER AFTER ONE HOUR OF STRUGGLING WITH IT ....
  FOR ALL THOSE GUYS WHO HAVE POSTED ANSWER 9/64 IS THE PROBABLITY OF EXACTLY 3 TRAILS NOT AT LEAST .....
  THE CORRECT ANSWER IS 11/16
  HERE IS THE SOLUTION ..
  PROB OF AT LEAST 3 DRAWS = 1 - ( PROBABILITY OF EXACTLY 2 DRAWS +PROBABILITY OF EXACTLY 1 DRAW)
  PROBABILITY OF EXACTLY 1 DRAW= HE DRAW A HEART IN 1ST GO
  P(1DRAW)= 13/52=1/4
  PROBABILITY OF EXACTLY 2 DRAW= HE DRAW A HEART IN SECOND GO
  P(2DRAW)= 39/52*13/52=3/16
  REQUIRED PROBABILITY = 1(1/4+3/16)
  = 1-7/16= 11/16
  HAVE FUN GUYS ITS CORRECT U CAN CHECK ITS ANSWER FROM ARUN SHARMA LOD 3 QUESTION 20
  
• 10 years agoHelpfull: Yes(16) No(14)
• Out of 52 cards there are 13 cards of heart
  other cards= 52-13= 39
  Probabality of making three trials-
  39/52*39/52*13/52=3/4*3/4*1/4=9/64
  Ans:9/64
• 10 years agoHelpfull: Yes(13) No(6)
• n first trial he drwas a heart is 1/4
  
  In second trial he draws a heart is 3/4*1/4
  
  The condition we require is disjoint with above case..So our prob is (1- 7/16)= 9/16
• 10 years agoHelpfull: Yes(9) No(10)
• here the no of trials is 3
  so lets take 2 times that he didn't succed
  so what will be its probility..??
  
  3/4 * 3/4
  now the third time he succeds.. and his probability will be 1/4
  so the solution shud be 3/4 * 3/4* 1/4
• 10 years agoHelpfull: Yes(7) No(5)
• Out of 52 cards there are 13 cards of heart
  other cards= 52-13= 39.
  P(Atleast 3 trails) = 1-(P(1 trial) + P(2 trial))
  P(1 trial) = 13/52
  P(2 trial) = 39/52 * 13/52
  P(1 trial) + P(2 trial) = 1/4 + (3/4*1/4) = 7/16
  therefore, P(Atleast 3 trial) = 1- 7/16 = 9/16
  
  therefore ans is 9/16.
• 10 years agoHelpfull: Yes(4) No(0)
• I know that @Karthikeyank...but the ans was 11/16...how is it possible?
• 10 years agoHelpfull: Yes(2) No(2)
• plz gve proper answer.
• 10 years agoHelpfull: Yes(2) No(1)
• clearly it was given that he has to make 3 or more than 3 trails to win so,calculate probability of winning in exactly in 2 trails and subtract it from total probability.then the result will give us the probability of winning in 3 or more than 3 trails.
  
  
  probability of winning in exactly 2 trails is: (39/52)*(1/4)=13/56
  now subtract it from 1:1-(13/56)=43/56.
• 10 years agoHelpfull: Yes(0) No(3)
• probability for clearing atleast in 3 trials=1- probability for getting diamond exactly in two trials. p(getting exactly two trials is )=39/54*1/4=3/4*1/4=3/16
  1-3/16=13/16 13/16 is the ans
• 10 years agoHelpfull: Yes(0) No(0)
• 9/64 is the propr answer.......sure
  
• 10 years agoHelpfull: Yes(0) No(1)
• 10 min
  100*10*x=10*10*100
• 10 years agoHelpfull: Yes(0) No(0)
• SORRY FRIENDS PREVIOUS ANS IS WRONG CORRECT ANSWERE IS 1O MINUTES
  
• 10 years agoHelpfull: Yes(0) No(0)
• the correct answer is 11/16...
  he has to make at least 3 trails so 3 or more than 3 trails are needed ..
  this can be done in finding exactly 2 trails and subtracting it from 1...
  for exactly 2 trails the first card is not of heart
  p(not heart) = 39/52
  and second card is heart for sure p(heart)=13/52
  total =3/4*1/4= 3/16
  required probablity of at least 3 trails = 1-3/16
  
• 10 years agoHelpfull: Yes(0) No(1)
• the correct answer would be 9/16
  because here more than 3 trials are acceptable and it is given that the minimum no of trials should be 3
  so p of not heart is 3/4
  and p of heart is 1/4
  so 3/4*3/4*1/4+3/4*3/4*3/4*1/4=...................................................................... infinity trials
  so its a gp series
  so the probabilty required is=3/4*3/4*1/4*(1/(1-(3/4)))=9/16!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  
  
  
  
  
• 9 years agoHelpfull: Yes(0) No(0)
• possibilities--->hit fail fail , fail fail hit ,fail hit fail (hit-drawing heart , fail-drawing other than heart)
  
  hit fail fail--->1/4*3/4*3/4
  +
  fail hit fail--->3/4*1/4*3/4
  +
  fail fail hit--->3/4*3/4*1/4
  
  -----------------------------------------------
  =27/64
  
  ans=27/64
• 9 years agoHelpfull: Yes(0) No(0)
• For at least 3 trials, he has to fail at the first 2 attempts and then after that it doesn’t make a difference if he fails or wins at the 3rd or the subsequent attempts.
  Chance of success at any attempt = 1/4
  => chance of failure = 3/4
  => chance of failing in first 2 attempt = (3/4)2 = Chance of success at any attempt = 1/4
  => chance of failure = 3/4
  
  => chance of failing in first 2 attempt = (3/4)2 = 9/16.
  
• 9 years agoHelpfull: Yes(0) No(0)