Answer
E and F are independent
Work Step by Step
We know that two events A, B are independent if P(A∩B) = P(A).P(B)
So, E represents strings that contain odd 1's.
and F represents strings that start with 0.
Total possibilities with strings of length three = $2^{3}$ =8
Strings that contain odd 1's = (100),(010),(001),(111) = 4
P(E) = 4/8 = 1/2
Strings that start with 0 = (000),(001),(010),(011) = 4
P(F) = 4/8 =1/2
Strings with odd 1's and starting with 0 = (010),(001) = 2
P(E∩F) = 2/8 =1/4
$1/2\times1/2$ = 1/4
Hence
P(E)P(F) = P(E∩F)
Independent events
