An experiment is to flip a coin until you either get two heads in a row or two tails in a row. If that happens, you stop. Also, if you flip the coin four times without getting two in a row, you stop. Some possible sequences of flips are TT, THH and HTHT. How many different sequences of flips are possible in this situation?

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Ryan Newman · Accepted Answer

Let the sample state of different sequences possible be SLet the event of getting two heads or two tails within 2 flips be ALet the event of getting two heads or two tails within 3 flips be BLet  the event of getting two heads or two tails within 4 flips or not getting two heads or two tails within 4 flips be CThus,    S  =  A  +  B  +  C  A  =      H    H    ,    T    T    B  =      H    T    T    ,    T    H    H    C  =      T    H    T    T    ,    T    H    T    H    ,    H    T    H    T    ,    H    T    H    H   And  S  =      H    H    ,         T    T    ,         H    T    T    ,         T    H    H    ,         T    H    T    T    ,         T    H    T    H    ,         H    T    H    T    ,         H    T    H    H    n  (  S  )  =  8Hence, there are 8 different sequence of flips that are possible

An experiment is to flip a coin until you either get two heads in a row or two tails in a row. If th

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