Let fn be a s-algebra generated by n coin tosses find the

Question

Question: Let F_n = be a σ-algebra generated by n coin tosses. Find the smallest n such that the following event belongs to F_n:

(a) A = {the first occurrence of heads is preceded by no more than 10 tails};

(b) B = {there is at least 1 head in the sequence

(c) C = {the first 100 tosses produce the same outcome};

(d) D = {there are no more than 2 heads and 2 tails among the first 5 tosses}.