A coin is tossed 
times, where 
. The probability of getting at least 
consecutive heads if 
and 
is 
. Find 
.
Text Solution
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12
Here 
and 
where 
denotes head or tail.
If the sequence of 
consecutive heads starts from the first throw, we have
times 
times 
Chance of this event 
times 
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, thefirst 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 tailbut 
throw must be a tail and we have,
times 
times 
The chance of this event also 
Since all the above events are mutually exclusive, so the required probability
times 
Note: Students should remember this question as a formula.
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