Probability of dependent events?

[horsewoman27]

A department store is holding a drawing to give free shopping sprees to two lucky customers. There are 15 customers who have entered the drawing: 4 live in the town of Gaston, 6 live in Pike, and 5 live in Wells. In the drawing, the first customer will be selected at random, and then the second customer will be selected at random from the remaining customers. What is the probability that both customers selected are Wells residents?

Report your answer as an exact fraction.

What is the formula for dependent events? I only can locate independent events. Thanks

 

[galactus]

Dependent essentially mean without replacement in this case.

The probability the first winner is from Wells would be 5/15=1/3

Now, since there is one less from Wells and one less total to draw from, the probability the next winner is from Wells would be 4/14=2/7. Assuming the first winner is from Wells.

So, \(\displaystyle \frac{1}{3}\cdot \frac{2}{7}=\frac{2}{21}\)

That is the dependence. The drawing of the second depends on the first because they are not replaced.

Now, if somehow there were replacement, then it would be independent. As in cards, for instance.

If the card were not put back in the deck, the second draw would be dependent. If it were put back, then independent.

See what I am getting at?. Taking something out and not replacing it changes the probability.