There are 3 boxes. Each box has 2 balls. Box1: white, white. Box2: white, black. Box3: black, black.
You don’t know which box is box1, box2 or box3. All you did was getting a ball from a random box in front of you. And you got a white ball. What’s the probability of getting another white ball?
Please consider both situations: 1. You put the first white ball back to the box. 2. You discard the first white ball.
My thoughts: 1. First time you get a white ball 1/2 * second time you get a white ball 1/2 = 1/4 2. Only box 1 is possible for getting 2 white balls. So 1/3.
Are they correct? If not please explain.