Latest TCS Aptitude Question SOLUTION: 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

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(#M40020089) TCS Numerical Ability question Keep an EYE

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

Asked In TCS Ish Mishra (10 years ago)

Unsolved Read Solution (10)

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Danish Shaikh   (10 years ago)

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

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Tanu  (10 years ago)

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

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Tanu  (10 years ago)

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!

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Tanu  (10 years ago)

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

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Kundan Kumar  (10 years ago)

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

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srimanti kar  (10 years ago)

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]

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juhe rawat  (10 years ago)

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

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rahul jha  (10 years ago)

answer=0.25
required probability=1-(24/2^5)

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kopparapuvyshnavi  (10 years ago)

could any one of you explain clearly plz....

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abhishek bhiwaniwala  (10 years ago)

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)...

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