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A fair coin is tossed `n` times. Let `a_(n)` denotes the number of cases in which no two heads occur consecutively. Then which of the following is not true ?A. `a_(1)=2`B. `a_(2)=3`C. `a_(5)=13`D. `a_(8)55` |
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Answer» Correct Answer - C `(c )` The cases for `a_(1){H,T}` i.e, `a_(1)=2` The cases for `a_(2){HT,TH,TT}`, `a_(2)=3` For `n ge 3` , if the first outcome is `H`, then next just `T` and then `a_(n-2)`. If the first out come is `T`, then `a_(n-1)` should follow. So, `a_(n)=1xx1xxa_(n-2)+1xxa_(n-1)impliesa_(n)=a_(n-2)+a_(n-1)` So, `a_(3)=a_(1)+a_(2)=5`, `a_(4)=3+5=8` and so on. |
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