Question

What is the probability of tossing an unfair coin 19 times and having heads come up 12 or more times (P(T)=0.7)?

Answer 1

Let X denote the number of times heads comes up in the 19 tosses.

Then

X ~ Bin(n = 19,p=1-0.7 = 0.3)

$P(X=x)=\binom{19}{x}(0.3)^x(1-0.3)^{19-x},x=0,1,2,..19$

Required probability =

$P(X\geq 12)=\sum_{x=12}^{19}\binom{19}{x}(0.3)^x(1-0.3)^{19-x}=0.0028$