Please help with the following binomial question!

Question

1.It is estimated that 18% of drivers do not signal while changing lanes.

Lisa stands at a stop sign, inspecting the first 30 vehicles to see if they have signaled or not.

What are the chances that no more than six cars will fail to signal?

Please show all steps.

Answer 1

P(X≤ 6) = P(X = 0) + P(X = 1 + P(X = 2) + ... + P(X= 6)

p = 0.18, q = 1 - p = 0.82;

P(X ≤ 6) = C(30,0)·0.18⁰·0.82³⁰ + C(30,1)·0.18·0.82²⁹ + C(30, 2)·0.18²·0.82²⁸+ C(30, 3)·0.18³·0.82²⁷+

C(30, 4)·0.18⁴·0.82²⁶ + C(30,5)·0.18⁵·0.82²⁵ + C(30, 6)·0.18⁶·0.82²⁴ = 0.0025966629 + 0.0170999751 +

+ 0.0544279696 + 0.1115109622 + 0.1652266086 + 0.1886001289 + 0.1725001179 = 0.712