a) The probability of landing head = 1/2

Since each roll is independednt, then prbability of landing heads 55 time or more = probability of landing heads 55 times + probability of landing 56 times + ...+ probability of langing heads 100 times

= (1/2)^55 + (1/2)^56 + ...+ (1/2)^100

= (1/2)^55 [ 1 + 1/2 + (1/2)^2 + ... + (1/2)^ 45]

B) Probability for getting between 40 and 6o tails = probability of getting 41 tails + P(42 tails) + ...+ P(59 tails)

= (1/2)^41 + (1/2)^42 + .... (1/2)^59)