it has been reported that 25 of all cars on the highway are

it has been reported that 25% of all cars on the highway are traveling at speeds in excess of 70 mph. if the speeds of 7 random automobiles are measured via radar:
a. what is the probability that exactly 3 cars are speeding?
b. what is the probability that at least one car is going over 70 mph.

Solution

a) P( 3 speeding) = 0.25^3 * (0.75)^3 = 27/4096

b) P(at least one speeding) = 1 - P(no one is speeding) = 1 - 729/4096 = 3367/4096 = 0.82202