Find probability of event “during the tossing of a symmetrical coin a series of three tails didn't...











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Let $a_n$ be probability of event "during n tossings of a symmetrical coin a series of three tails didn't appear". Find $a_n$ for n=1,...,12.$$$$
I know, here I need to apply recursive equations. But I don't understand how.










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  • to count the binary strings of length $n$ without a $TTT$ note that, for $n>2$, such a string must end in one of $H, HT,HTT$.
    – lulu
    Nov 14 at 15:14

















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down vote

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Let $a_n$ be probability of event "during n tossings of a symmetrical coin a series of three tails didn't appear". Find $a_n$ for n=1,...,12.$$$$
I know, here I need to apply recursive equations. But I don't understand how.










share|cite|improve this question
























  • to count the binary strings of length $n$ without a $TTT$ note that, for $n>2$, such a string must end in one of $H, HT,HTT$.
    – lulu
    Nov 14 at 15:14















up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let $a_n$ be probability of event "during n tossings of a symmetrical coin a series of three tails didn't appear". Find $a_n$ for n=1,...,12.$$$$
I know, here I need to apply recursive equations. But I don't understand how.










share|cite|improve this question















Let $a_n$ be probability of event "during n tossings of a symmetrical coin a series of three tails didn't appear". Find $a_n$ for n=1,...,12.$$$$
I know, here I need to apply recursive equations. But I don't understand how.







probability






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edited Nov 14 at 15:15

























asked Nov 14 at 15:12









Emerald

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  • to count the binary strings of length $n$ without a $TTT$ note that, for $n>2$, such a string must end in one of $H, HT,HTT$.
    – lulu
    Nov 14 at 15:14




















  • to count the binary strings of length $n$ without a $TTT$ note that, for $n>2$, such a string must end in one of $H, HT,HTT$.
    – lulu
    Nov 14 at 15:14


















to count the binary strings of length $n$ without a $TTT$ note that, for $n>2$, such a string must end in one of $H, HT,HTT$.
– lulu
Nov 14 at 15:14






to count the binary strings of length $n$ without a $TTT$ note that, for $n>2$, such a string must end in one of $H, HT,HTT$.
– lulu
Nov 14 at 15:14

















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