A coin is weighted so that the probability of heads on any flip is 0.7, while the probability of tails is 0.3. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice? Choose the correct option:
A) (0.7)^5 + 5(0.7)^4(0.3) + 10(0.7)^3(0.3)^2
B) (0.7)^5 + 4(0.7)^4(0.3) + 6(0.7)^3(0.3)^2
C) (0.7)^5 + 3(0.7)^4(0.3) + 2(0.7)^3(0.3)^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) = 0.7   Probability of Tail, P(T) = 0.3   Tail will appear NO more than twice   i.e. favourable cases   2 Tails and 3 Heads, Probability = 5C2*(0.7)^3*(0.3)^2   1 Tail and 4 Heads, Probability = 5C1*(0.7)^4*(0.3)^2   0 Tail and 5 Heads, Probability = (0.7)^5   Required Probability = Sum of all Favourable cases = (0.7)^5 + 5(0.7)^4(0.3) + 10(0.7)^3(0.3)^2   (0.7)^5 + 5(0.7)^4(0.3) + 10(0.7)^3(0.3)^2nswer: option (0.7)^5 + 5(0.7)^4(0.3) + 10(0.7)^3(0.3)^2
<result>A</result>
A coin is weighted so that the probability of heads on any flip is 0.7, while the probability of tails is 0.3. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?