Question

The probability of any standard traffic light that you would approach when travelling through town being red is 40%. Given that you hit 5 lights on the way to school, calculate the following:
a. The probability that you hit 0 red lights is
b. The probability that you hit 3 or more red lights is:
c. The expected number of red lights you would hit is:

Answer 1

There is a binomial distribution with p=0.4 and n=5.

a. $P(X=0)=C^0_n0.4^0(1-0.4)^5=0.0778.$

b. $P(X\ge3)=P(X=3)+P(X=4)+P(X=5)=$

$C^3_50.4^3(1-0.4)^2+C^4_50.4^4(1-0.4)^1+C^5_50.4^5(1-0.4)^0=0.3174.$

c. $E(X)=pn=0.4*5=2.$