A magician designed an unfair coin so that the probability of getting a Head on a flip is 60%. If he flips the coin three times, what is the probability that he flips more Heads than Tails? Express your answer as a common fraction.
"More heads than tails" means these possibilities :
2 Heads - 1 Tail
3 Heads - 0 Tails
Probability of 2 Heads - 1 Tail = C(3,2) (.60)^2 (.40) = 3 * (.36)(.40) = 3 * .144 = 3 (144/1000) = 3 ( 18/125) =
54/125
Probability of 3 Heads = (.60)^3 = .6 (.36) = .216 = 216 / 1000 = 27 / 125
So....the total probability = 54 / 125 + 27 / 125 = 81 / 125