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I got confusion !

Does it mean "two successive tosses is the same" is same as "two successive tosses is either heads or tells" ?

I have two problems :

Q. I have an unbiased coin , assuming that the trials are independent, find the the expected number of tosses ? when unbiased coin is tossed repeatedly until the outcome of two successive tosses is____ .

  1. Same
  2. Either heads or tells

I have try to solve problems , I applied same logic .that's fine . answer will be Q.(2) 6 {e=2$^N$$^+$$^1$−2}but for Q.(1) 6(tells)+6(heads) = 12 times ?{but this question appear on a competitive and answer gives 3 } Please do not give "down vote" , This is not homework question ,I found from defferent -2 sources . Is it right , same = (heads +tells)/2 ? I need explanation for both .

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Mithlesh Upadhyay
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1 Answers1

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The English in the problem is not as clear as it might be.

I think (2) asks for the waiting time to get HH (two Heads in a row). From the referenced page on this site you have found that the answer is 6.

Or, equivalently (2) could be interpreted as the waiting time to get TT. By symmetry (fair coin) this as also 6.

I think (1) asks for the waiting to get either HH or TT. That gives two ways to satisfy the criterion to stop, so stopping will be sooner, not later. Intuitively, 3 (as in the answer provided.

For a formal derivation of (1), you could modify the argument used in the referenced page.

BruceET
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