Smoking v. Speeding

Action for damages and personal injuries received by P when the car that P was driving collided with D's car at 7:30 P.M. on Saturday, June 1, at an intersection controlled by a traffic light. P claims that she was proceeding through a green light when D's car struck her from the right. D claims that P ran a yellow light and that D had the green light while in the intersection. There were no eyewitnesses to the accident other than the drivers.

At the trial, D offers the testimony of P's roommate, W, a hostile witness, that on the night in question, P was on her way to a movie and that P generally smoked several marijuana cigarettes immediately before or on the way to movies. P offers evidence showing that D has been cited eight times in the past two years for going through red lights and that three of those citations were given after automobiles driven by D had been involved in collisions with other vehicles.

Is any of this evidence admissible? Why?