Please show all work Suppose an unfair coin comes up tails 3

Please show all work.

Suppose an unfair coin comes up tails 34.7% of the time if it is flipped. If the coin is flipped 14 times, what is the probability that:

a) it comes up heads exactly 8 times?

b) it comes up tails more than 12 times?

The number of tails is a Binomial Distributed variable with n=14 and p = 0.347

a. P(Heads = 8) = P(Tails = 14-8=6)

= 14C6 * (0.347)⁶ * (1-0.347)^14-6 = 0.1733

b. P(Tails > 12) = P(Tails = 13) + P(Tails = 14)

= 14C13 * (0.347)¹³ * (1-0.347)^14-13 + 14C14 * (0.347)¹⁴ * (1-0.347)^14-14

= 0.00001003468