A bag contains five white balls and three black balls. Your goal is to draw two white balls.
(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls at random. Once you have drawn two balls, you put back any black balls, and redraw so that you again have two drawn balls. What is the probability that you now have two white balls? (Include the probability that you chose two white balls on the first draw.)
(a) The probability is 4/25.
(b) The probability is 8/125.
I disagree with the first one, I got:
Let's start with what probability is, probability is:
So let's find the total of picking two random balls. We have 8 balls at the start, so 8 options, then after we picked one, we can only pick 7, so 7 options. To draw both white balls, you have to pick one of the 5, and then one of the 4 that are left. So here, the probability for this one is:
So the probability for the first one is 5/14.
I don't know if I disagree with the second one, cause I haven't thought of that one yet... (aka, I don't know if I should use casework or something else)