A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

$\text{ Let }H\text{ denote the head, }T\text{ the tail and }\ast \text{ any of the head }$$\text{ or tail. Then, }P\left(H\right)=1/2,P\left(T\right)=1/2\text{ and }P(\ast )=1\text{. For at least }$

$\text{ four consecutive heads, we should have any of the following }$

patterns:

Since all the above cases are mutually exclusive, the probability of getting at least four consecutive heads (on adding) is
$1/16+3/32=5/32$