Answer:
Required probability = 0.8131
Step-by-step explanation:
We are given that 90 percent of automobiles in Orange County have both headlights working.
Also, a sample of eight automobiles is taken.
Firstly, the binomial probability is given by;

where, n = number of trails(samples) taken = 8
r = number of successes
p = probability of success and success in our question is % of
automobiles in Orange County having both headlights working
i.e. 90%.
Let X = Number of automobiles in Orange County having both headlights working
So, X ~ 
So, probability that in a sample of eight automobiles, at least seven will have both headlights working = P(X >= 7)
P(X >= 7) = P(X = 7) + P(X = 8)
=
=
= 0.3826 + 0.4305 = 0.8131 .