You have a box in your room full of calculator batteries. You were not careful and put the good ones and the bad ones together and now you cannot tell them apart. You need to find two good batteries for your new calculator so that you can do your statistics homework. You know that in the box you had 4 good batteries and 7 bad batteries. You take one battery at a time and test to see if it works Use this information to answer the next five questions.
Is this an example of drawing with replacement, drawing without replacement, or neither?

You take out one battery. How many possible outcomes are in the sample space?

What is the probability that the first battery you take out is good? Enter your answer as a fraction.

What is the probability that the second battery you take is good? Enter your answer as a fraction. (Hint: think about how the sample space changes after taking out one battery).

The probability you found in the previous question was the probability that the second battery you take out is good given that the first battery your took out was good. Can you see why this is true?

With that in mind, what is the probability that you take two batteries out of the box and both are good? Enter your answer as a fraction.