madeeasytest

Question

a coin tossed nine time .what is the probability that only first two tosses will yield tails? 

Comments

$\frac{1}{512}$

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it will look like, $TTHHH....H$ and hence probability = $\frac{1}{2^9}$

Answer 1

A fair coin is tossed 9 times,what is the probability that tail will come up in first two toss of coin"

We do not even need to consider remaining tosses.

So Total Set of outcomes of First 2 tosses is = ${ HH,HT,TH,TT}$

Required outcome = ${TT}$

Answer -> cardinality ${TT}$ / cardinality ${HH,HT,TH,TT} = 1/4 = 0.25$

Comments

sir i am in confusion. what answer will correct above these?

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$\frac{1}{2^9}$ is correct

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How? and what is the mistake in my approach?

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sandeep ...just think about  the complement of the statement ...then that must be equal to (1-this probability) ...

then u will come to know ur mistake.....

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@Sandeep Suri,

actual qsn is -> what is the probability that only first two tosses will yield tails?

and you are answering for,

what is probability that first two tosses will yield tails?

 hope you got :)

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You are tossing only two times while question ask for 9 times.

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Question is being asked for first 2 toss not about 9. Therefore I considered only 2 tosses. Hope you got this.. Please correct me if I am wrong.

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A coin tossed nine time . Read question 1st statement. there is no point of argument here . 

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@Sandeep Suri

A fair coin is tossed 9 times,what is the probability that tail will come up in first two toss of coin"

We do not even need to consider remaining tosses.

why you don't care ?

according to you, $TTTTTTTTT,\ TTHTTTTTT $ any more are required outcomes, but it is wrong, because doing so tails will come in other positions also(except first 2 tosses), but in qsn it is said that "only first two tosses should be tails"

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check this i guess it will clear the doubt @anu @joshi

https://gateoverflow.in/19730/probability

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@Aditya Tewari,

without seeing entire conversation, you posted that link, i guess.

a coin tossed nine time .what is the probability that only first two tosses will yield tails? 

see the highlighted word here and compare it with one whose link you have posted. 

the word 'only' is the cause of different answer.

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@joshi...did read the thread btw

yes yes...i see now.....now i get you clearly...thanks for pointing out...:)

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If you for 9 tosses also answer will be the same.

If you tossed 9 times then the out come possible are : 2^9

We have to find the possibilities by putting first and second toss as Tail so : TT------- (2^7 possibilities are there). First 2 tosses result is TAIL and remaining tosses output can be anything so 2^7 possibilities).

 

P(first 2 tosses Tail)=possibilities of TT-------/total no. of possibilities

=(2^7)/(2^9)

=1/(2^2)

=1/4

=0.25