Latest TCS Aptitude Question SOLUTION: 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

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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 ?

Asked In TCS vaibhav sharma (11 years ago)

Unsolved Read Solution (16)

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Read Solution (16) :

Ravi  (11 years ago)

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.

Is this solution Helpfull? Yes (33) | No (6)  

Parijat Mukherjee  (11 years ago)

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

Is this solution Helpfull? Yes (17) | No (2)  

lala  (11 years ago)

@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

Is this solution Helpfull? Yes (8) | No (4)  

Parijat Mukherjee  (11 years ago)

The second flip is completely an independent event. So....probability of getting is 1/2.

Is this solution Helpfull? Yes (2) | No (5)  

snehil  (11 years ago)

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

Is this solution Helpfull? Yes (2) | No (11)  

tamil selvan  (11 years ago)

answer: 1/4

Is this solution Helpfull? Yes (1) | No (9)  

Ashok  (11 years ago)

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

Is this solution Helpfull? Yes (1) | No (6)  

shashank kansal  (11 years ago)

show the proper method..

Is this solution Helpfull? Yes | No (2)  

sameer  (10 years ago)

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.

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khan kashif tasneem  (9 years ago)

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

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khan kashif tasneem  (9 years ago)

sorry i thought there were 3 coins...
1/2+1/2*1/2 = 3/4 ...
correct answer

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Puneet Srivastava  (8 years ago)

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

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Priyanka   (8 years ago)

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

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CHANDRANI MONDAL  (8 years ago)

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

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Shashank Sourabh Singh  (8 years ago)

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

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Shah Heli  (8 years ago)

Total Case: {H,H,T}*{H,H,T}=HH,HH,HT,HH,HH,HT,TH,TH,TT
So Probability= 6/8=3/4

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