Question

A biased coin is tossed 5 times where p(t) = .6. determine the probability that if you have 2 tails, you have 3 tails.

Answer 1

It is a binomial distribution, with
p=0.6 (probability of success)
q=0.4 (probability of failure)
n=5 (number of steps)
r=2 or 3 (number of successes)

P(n,r)=nCr p^r q^(n-r)
P(5,2)=5C2 0.6^2 0.4^3
=(5!)/(3!2!) 0.6^2 0.4^3
= 10(0.36)(0.064)
= 0.2304

Similarly, for 3 tails, r=3,
P(5,3)=.3456

Answer 2

thanks so much!