A coin is weighted so that the probability of heads on any flip is 0.4, while the probability of tails is 0.6. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?  Choices
A) (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2 B) (0.6)^5 + 4(0.6)^4(0.4) + 6(0.6)^3(0.4)^2 C) (0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2 D) (0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2 E) (0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
Probability of Head, P(H) = 0.4   Probability of Tail, P(T) = 0.6   Tail will appear NO more than twice   i.e. favourable cases   2 Tails and 3 Heads, Probability = 5C2*(0.4)^3*(0.6)^2   1 Tail and 4 Heads, Probability = 5C1*(0.4)^4*(0.6)^2   0 Tail and 5 Heads, Probability = (0.4)^5   Required Probability = Sum of all Favourable cases = (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2   (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2nswer: option (0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2
<result>A</result>
A coin is weighted so that the probability of heads on any flip is 0.4, while the probability of tails is 0.6. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?