Question 778464
A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 4 times, what is the probability of getting
P(H) = 2P(T)
P(H) + P(T) = 1
2P(T) + P(T) = 1
3P(T) = 1
P(T) = {{{1/3}}} and P(H) = {{{2/3}}}

a. exactly 2 tails?
X~Binomial(4, 1/3)
P(X = 2) = {{{(matrix(2,1,4,2))(1/3)^2*(2/3)^2}}} = {{{highlight(0.2963)}}}

b. at least 3 heads?
Y~Binomial(4, 2/3)
P(Y≥3) = {{{(matrix(2,1,4,3))*(2/3)^3*(1/3)^1 + (matrix(2,1,4,4))*(2/3)^4*(1/3)^0 }}} = {{{highlight(0.5926)}}}