Statistics Probability: 4 people are at a car showroom. They may purchase the car (denoted as P) or may not (denoted as N). What is the probability that (A) exactly 3 people will purchase a car, (B) 3 or fewer people will purchase a car, (C) 1 or more people will purchase a car, and (D) all four people make the same purchase decision?

Question

anonymous · Answer

What is the probability that they purchase the car?  Is it equally probable that they do or do not buy it?

anonymous · Answer

they are equally liekly  to purchase the vehicle

anonymous · Answer

Okay.
Now, the events that someone buys the car is independent of whether or not other people buy the car.  So for each person who buys a car, you multiply $\large \frac{1}{2}$.

anonymous · Answer

Also, the event that 2 people buy a car and the event that more or less than 2 people buy a car can not happen at the same time.  They are mutual exclusive events.  So to find the probability that either happen, you add them up.

anonymous · Answer

So for example, the probability that less than 3 people buy the car is the probability that 1 person buys a car OR that 2 people buy a car.  So we have $\frac{1}{2} + \frac{1}{2} \cdot \frac{1}{2}$

anonymous · Answer

Are you following me so far?

anonymous · Answer

One last thing to remember is that probability that an event DOESN'T happen is just one minus the probability that it does.  So the probability that you don't have 3 people buy the vehicle is $1 - \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$.