A coin is tossed 
times, where 
The probability of getting at least m consecutive heads is
Text Solution
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Here 
and 
where 
denotes head or tail.
If the sequence of 
consecutive heads starts from the first throw, we have 
.
Chance of this event 
and subsequent throws may be head or tail since we are considering at least 
consecutive heads. If the sequence of 
consecutive heads starts from the second throw, the first must be a tail and we have, the chance of this event 
If the sequence of heads starts from 
throw then the first 
throws may be head or tail but 
throw must be a tail and we have,
The chance of this event also 
Since all the above events are mutually exclusive, so the required probability 
.
Note : Students should remember this question as a formula.
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