Latest TCS Aptitude Question SOLUTION: 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?

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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?

Asked In TCS Gourab Dutta (9 years ago)

Unsolved Read Solution (17)

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Read Solution (17) :

karthikeyank  (9 years ago)

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

Is this solution Helpfull? Yes (52) | No (15)  

ankit  (9 years ago)

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

Is this solution Helpfull? Yes (16) | No (14)  

Samruddhi Ganpat Patankar  (9 years ago)

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

Is this solution Helpfull? Yes (13) | No (6)  

karthikeyank  (9 years ago)

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

Is this solution Helpfull? Yes (9) | No (10)  

ranjan kumar  (9 years ago)

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

Is this solution Helpfull? Yes (7) | No (5)  

Sayan Choudhury  (9 years ago)

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.

Is this solution Helpfull? Yes (4) | No   

Gourab Dutta  (9 years ago)

I know that @Karthikeyank...but the ans was 11/16...how is it possible?

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

keerthi  (9 years ago)

plz gve proper answer.

Is this solution Helpfull? Yes (2) | No (1)  

rama   (9 years ago)

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.

Is this solution Helpfull? Yes | No (3)  

janani priya  (9 years ago)

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

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SHUBHAM  (9 years ago)

9/64 is the propr answer.......sure

Is this solution Helpfull? Yes | No (1)  

smdp  (9 years ago)

10 min
100*10*x=10*10*100

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sandeep kumar  (9 years ago)

SORRY FRIENDS PREVIOUS ANS IS WRONG CORRECT ANSWERE IS 1O MINUTES

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ankit  (9 years ago)

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

Is this solution Helpfull? Yes | No (1)  

supriyo das  (8 years ago)

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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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koora bhavya sri  (8 years ago)

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

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Brajeshrai  (8 years ago)

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.

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