A traffic light at a certain intersection is green 50% of the time, yellow 10% of the time, and red 40% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.

a. Find P (X = 3)
b. Find P (X =< 3).

c. Find μx

d. Find σx2



Detail is appreciated as i have worked on this problem and want to see how it is properly worked out and to check for mistakes.

Thanks,

Aphareus