1.

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 ?

Answer»

`a_(1)=2`
`a_(2)=3`
`a_(5)=13`
`a_(8)=55`

SOLUTION :`(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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